DOSEN PROFIL LENGKAP

In category theory, the coproduct, or categorical sum, is a construction which includes as examples the disjoint union of sets and of topological spaces...

(also called the direct sum, free union, free sum, topological sum, or coproduct) of a family of topological spaces is a space formed by equipping the...

category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the colimit...

disjoint sets is their union. In category theory, the disjoint union is the coproduct of the category of sets, and thus defined up to a bijection. In this context...

a generalization of mathematical products Fibre product or pullback Coproduct or pushout Wick product of random variables Graph product Product (Brand...

zero objects, is both a product and a coproduct. In a preadditive category the notions of product and coproduct coincide for finite collections of objects...

the coproduct in the category of the mathematical objects in question. For example, in the category of abelian groups, the direct sum is a coproduct. That...

F} yields a coproduct C ∗ ( X ) → C ∗ ( X ) ⊗ C ∗ ( X ) {\displaystyle C_{*}(X)\to C_{*}(X)\otimes C_{*}(X)} inducing the standard coproduct on H ∗ ( X...

monoidal unit. Dually, a monoidal finite coproduct category with the monoidal structure given by the coproduct and unit the initial object is called a...

produced naturally on a large scale in volcanoes. It is manufactured as a coproduct in the production of phosphate fertilizers. The resulting hexafluorosilicic...

(and for representation theory in general), the coproduct must be linear. As a general rule, the coproduct in representation theory is reducible; the factors...

unital and associative. The unit is explicitly required to define the coproduct. Let V be a vector space over a field K. For any nonnegative integer k...

describes a slight variant of this Hopf algebra using the opposite coproduct, i.e. the coproduct described above composed with the tensor flip on H4⊗H4. This...

is dual to a coproduct defined on ⁠ ⋀ ( V ) {\displaystyle \textstyle \bigwedge (V)} ⁠, giving the structure of a coalgebra. The coproduct is a linear...

beverages. tert-Butyl alcohol is derived commercially from isobutane as a coproduct of propylene oxide production. It can also be produced by the catalytic...

universal group with a given set of generators). The free product is the coproduct in the category of groups. That is, the free product plays the same role...

family (Ai) of objects of A, the coproduct *Ai exists in A (i.e. A is cocomplete). AB4) A satisfies AB3), and the coproduct of a family of monomorphisms is...

component-wise. The coproduct of a family of rings exists and is given by a construction analogous to the free product of groups. The coproduct of nonzero rings...

colimit generalizes constructions such as disjoint unions, direct sums, coproducts, pushouts and direct limits. Limits and colimits, like the strongly related...

example of a product in a category, whereas a direct sum is an example of a coproduct. If R {\displaystyle \mathbb {R} } is thought of as the set of real numbers...

every finitary product is necessarily a coproduct, and hence a biproduct, and conversely every finitary coproduct is necessarily a product (this is a consequence...

amides into nitriles: P4O10 + RC(O)NH2 → P4O9(OH)2 + RCN The indicated coproduct P4O9(OH)2 is an idealized formula for undefined products resulting from...

fiber products distribute over coproducts; that is, given a set I {\displaystyle I} , an I {\displaystyle I} -indexed coproduct mapping to A {\displaystyle...

In algebra, the free product (coproduct) of a family of associative algebras A i , i ∈ I {\displaystyle A_{i},i\in I} over a commutative ring R is the...

converts to silicon dioxide: Si(OCH2CH3)4 → SiO2 + 2 (CH3CH2)2O The volatile coproduct is diethyl ether. Inhalation of TEOS induces eye and nose irritation,...

Among its coproducts in the process are feed ingredients such as distillers grains, syrup and corn oil, along with additional coproducts including an...

where the plus sign here denotes the coproduct. To see this, note that the universal property of the coproduct X × Y + X × Z {\displaystyle X\times Y+X\times...

Cartesian closed categories with binary coproducts and an initial object, with products distributing over coproducts. Their equational theory is extended...

submodules with no "unnecessary" constraints, making it an example of a coproduct. Contrast with the direct product, which is the dual notion. The most...

identity map is the unit. Dually, any category with finite coproducts is monoidal with the coproduct as the monoidal product and the initial object as the...

circles) gives a product map V ⊗ V → V {\displaystyle V\otimes V\to V} or a coproduct map V → V ⊗ V {\displaystyle V\to V\otimes V} , depending on how the boundary...

example, if C {\displaystyle {\mathcal {C}}} has finite products and coproducts, it is immediate the categories C / X {\displaystyle {\mathcal {C}}/X}...

of the limit, the result is the product; for the colimit, one gets the coproduct. So, for example, when J is the discrete category with two objects, the...

colimit of the empty diagram 0 → C and can be thought of as an empty coproduct or categorical sum. It follows that any functor which preserves limits...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

in a preadditive category must also be a coproduct, and conversely. In fact, finite products and coproducts in preadditive categories can be characterised...

coproduct in the category of commutative R-algebras. The tensor product is not the coproduct in the category of all R-algebras; there the coproduct is...

1-(trimethylsilyl)imidazole requires more preparative effort with the advantage that the coproduct trimethylsilyl chloride is volatile. CDI hydrolyzes readily to give back...

homomorphism. (A finite coproduct in the category of commutative algebras over a commutative ring is a tensor product of algebras. A coproduct in the category...

give both nitrous acid and nitric acid: N2O4 + H2O → HNO2 + HNO3 The coproduct HNO2 upon heating disproportionates to NO and more nitric acid. When exposed...

record, choice type, discriminated union, disjoint union, sum type, or coproduct, is a data structure used to hold a value that could take on several different...

also the pushout. Since the pushout in the category of rings, i.e, the coproduct in a category of algebras over a ring R, is given by the tensor product...

preparing certain nylons, is produced by cleavage of ricinoleic acid. The coproduct is 2-octanol. The mechanism of the base-induced cleavage is proposed to...

coproduct T o Δ, where T is given by T(x ⊗ y) = y ⊗ x, giving three more possible versions. The counit on Uq(A) is the same for all these coproducts:...

union An empty sum or empty coproduct An initial object in a category (an empty coproduct, and so an identity under coproducts) An absorbing element in a...

derived from oxygenation of isobutane, which affords t-butanol. This coproduct can be dehydrated to isobutene, converted to MTBE, an additive for gasoline...

chloride gas is dissolved in water to produce hydrochloric acid as a useful coproduct of the reaction. Sodium bisulfate can be generated as a byproduct of the...

x , y ∈ X {\displaystyle x,y\in X} . Here the Sweedler's notation of coproduct of Hopf algebra is used. For matched pair of Hopf algebras A {\displaystyle...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

in terms of projections from coproducts, having a family of projective generators along with the existence of coproducts guarantees the category has "enough...

isopropanol in presence of ammonia. Hydrogen chloride is formed as a coproduct: TiCl4 + 4 (CH3)2CHOH → Ti{OCH(CH3)2}4 + 4 HCl Titanium isopropoxide reacts...

manifolds), the map associated with a pair of pants gives a product or coproduct, depending on how the boundary components are grouped – which is commutative...

(equivalently, all finite coproducts); note that because C is also preadditive, finite products are the same as finite coproducts, making them biproducts;...

1965) is the founder of POET, LLC, a leading producer of biofuels and coproducts. He currently serves as chairman and CEO. Broin's family ran a farm in...

} is a type with no terms. Such a type may be defined as the nullary coproduct (i.e. disjoint sum of no types). It may also be defined as the polymorphic...

commutative diagrams:                                        Now use the coproduct (the disjoint union of sets) to glue the three morphisms in one: α = e...

is usually taken to be a finite-dimensional algebra and coalgebra with coproduct Δ: H → H ⊗ H and counit ε: H → k satisfying all the axioms of Hopf algebra...

dimerization of butadiene in the presence of a nickel or iron catalyst, a coproduct being vinylcyclohexene. Approximately 10,000 tons were produced in 2005...

of the symmetric group. The ring of symmetric functions can be given a coproduct and a bilinear form making it into a positive selfadjoint graded Hopf...

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built up inductively with the nth item in the resolution equal to the coproduct of the nth items in the resolutions of A ′ {\displaystyle A'} and A ″...

sum of the underlying spaces. The wedge sum can be understood as the coproduct in the category of pointed spaces. Alternatively, the wedge sum can be...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

alcohol (typically methanol or ethanol) to produce biodiesel and an impure coproduct, glycerol. If the feedstock oil is used or has a high acid content, acid-catalyzed...

) {\displaystyle D(x,x^{\prime })=(dx,d^{\prime }x^{\prime })} . The coproduct of two differential graded Lie algebras, L ∗ L ′ {\displaystyle L*L^{\prime...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

including exports of corn silage and dried distiller grains (ethanol coproducts). As a grain crop, the dried kernels are used as feed. They are often...

_{R}\to \mathbf {Mod} _{S}} is additive, is right-exact and preserves coproducts if and only if it is of the form F ≃ − ⊗ R F ( R ) {\displaystyle F\simeq...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

∇ Del operator Gradient Divergence Curl ∈ Element (mathematics) ƛ Reduced wavelength ∐ Coproduct...

of the simply typed lambda calculus with constructs such as products, coproducts or natural numbers (System T) or even full recursion (like PCF). In contrast...

category D. Split coequalizers are examples of absolute coequalizers. Coproduct Pushout Barr, Michael; Wells, Charles (1998). Category theory for computing...

not cartesian closed. In a category with a terminal object 1 and binary coproducts (denoted by +), an NNO can be defined as the initial algebra of the endofunctor...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

same stereoselectivity as metal-catalysed syn addition of H2. The only coproduct released is nitrogen gas. Although the method is cumbersome, the use of...

compared to fish-fed salmon. Another possible alternative is a yeast-based coproduct of bioethanol production, proteinaceous fermentation biomass. Substituting...

and only if it has coequalizers and all (small) coproducts, or, equivalently, pushouts and coproducts. Finite completeness can be characterized in several...

product of sets. The coproduct is given by the disjoint union: given sets Ai where i ranges over some index set I, we construct the coproduct as the union of...

case of the coproduct operation, and general coproducts are perhaps the most abstract of all the generalizations of addition. The coproduct such as direct...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

i)\mid i\in {\mathcal {I}}\land a\in A_{i}\}.} The disjoint union is the coproduct in the category of sets. Therefore the notation ∐ i ∈ I = { ( a , i )...

into another category is called a product, while the colimit is called a coproduct. Thus, for example, the discrete category with just two objects can be...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Food versus fuel is the dilemma regarding the risk of diverting farmland or crops for biofuel production to the detriment of the food supply. The biofuel...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

"Identification of Guayule Regions in Northern Mexico, Based on Rubber Yield and Coproducts Quality". hort.purdue.edu. "Guayule Production: Rubber and Biomass Response...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Ozonolysis of oleic acid is an important route to azelaic acid. The coproduct is nonanoic acid: CH3(CH2)7CH=CH(CH2)7CO2H} + 4 O3 → HO2C(CH2)7CO2H} +...

_{1}(X)\otimes I+I\otimes \phi _{2}(X)} . This product can be recognized as the coproduct on a coalgebra. In general, the tensor product of irreducible representations...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

erucic acid, which is abundant in some seed oils. Pelargonic acid is the coproduct. In the industrial setting, brassylic acid is used to produce specialty...

as the allocation of GHG emissions to the management and the use of coproducts can have a large effect on the total carbon footprint of resulting bioenergy...

⨆ i ∈ I A i . {\textstyle \bigsqcup _{i\in I}A_{i}.} 2.  Denotes the coproduct of mathematical structures or of objects in a category. よ    (Hiragana...

(to be precise, has some pre-additive structure) and admits all finite coproducts. Although "preadditive" is an additional structure, one can show "additive"...

S → S ⊗ S , {\displaystyle \Delta \colon S\to S\otimes S,} called the coproduct, such that Δ ( X ) = X ⊗ 1 + 1 ⊗ X {\displaystyle \Delta (X)=X\otimes...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

V\in {}_{H}^{H}{\mathcal {YD}}} is always a braided Hopf algebra. The coproduct Δ {\displaystyle \Delta } of T V {\displaystyle TV} is defined in such...

realizer of y {\displaystyle y} . The coproduct of X {\displaystyle X} and Y {\displaystyle Y} is the coproduct of sets X + Y {\displaystyle X+Y} where...

product of the images; applying a left adjoint functor to a coproduct of objects yields the coproduct of the images; every right adjoint functor between two...

} is just the direct product of groups while the category-theoretical coproduct in G r p {\displaystyle \mathbf {Grp} } is the free product of groups...

in a tremendous release of ring strain, the former with nitrogen gas coproduct. Epoxides typically give reactive carbonyl wastes, and asymmetric epoxides...

preadditive. If, furthermore, the category has all finite products and coproducts, it is called an additive category. If all morphisms have a kernel and...

infinite) family of objects in A {\displaystyle {\mathcal {A}}} has a coproduct (also known as direct sum) in A {\displaystyle {\mathcal {A}}} ; direct...

theory) (also called an amalgamated sum or a cocartesian square, fibered coproduct, or fibered sum), the colimit of a diagram consisting of two morphisms...

of the arrows. Each category J can be written as a disjoint union (or coproduct) of a collection of connected categories, which are called the connected...

(category theory)/fiber product Inverse limit Pro-finite group Colimit Coproduct Coequalizer Cokernel Pushout (category theory) Direct limit Biproduct...

addition and multiplication, can be seen as carrying information about coproducts and products of the category of finite sets. Less abstractly, the idea...

via the methylation of methionine by S-adenosyl methionine (SAM). The coproduct is S-adenosyl homocysteine. The biological roles of S-methylmethionine...

The category of pointed sets and pointed maps has both products and coproducts, but it is not a distributive category. It is also an example of a category...

Oxidative coupling of phenol by VCl4. Coproducts including vanadium(III) and hydrogen chloride are not shown...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

X_{i}} contain a nonzero element, the Lp sum is neither a product nor a coproduct. Helemskii, A. Ya. (2006). Lectures and Exercises on Functional Analysis...

Industrial Organic Chemicals (2 ed.). Wiley-Interscience. pp. 236–7. ISBN 978-0-471-44385-8. Retrieved 2009-04-19. 6. https://nctius.com/op-coproduct-streams/...

mixtures of methane or methyl chloride with chlorine. Dichloromethane is a coproduct. Bromochlorofluoromethane is one of the simplest possible stable chiral...

or variables)Pages displaying short descriptions of redirect targets Coproduct – Category-theoretic construction Diagram (category theory) – Indexed...

Ozonolysis of oleic acid is an important route to azelaic acid. The coproduct is nonanoic acid: H17C8CH=CHC7H14CO2H + 4"O" → HO2CC7H14CO2H + H17C8CO2H...

it is a presentable ∞-category, (2) colimits in X are universal, (3) coproducts in X are disjoint and (4) every groupoid object in X is effective. Mathematics...

of finite sets. Dually, the coproduct of an empty family is an initial object. Nullary categorical products or coproducts may not exist in a given category;...

( ξ n ) = 2 n − 1 {\displaystyle \deg(\xi _{n})=2^{n}-1} . Then, the coproduct map is given by Δ : A ∗ → A ∗ ⊗ A ∗ {\displaystyle \Delta :{\mathcal {A}}_{*}\to...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

ΔX : X → X × X. Dually in a category with an initial object and finite coproducts every object becomes a monoid object via idX ⊔ idX : X ⊔ X → X. Given...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

left-adjoint of the binary product functor and the right-adjoint of the binary coproduct functor. Diagram (category theory) Cone (category theory) Diagonal morphism...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

simply connected. Coproduct topology If {Xi} is a collection of spaces and X is the (set-theoretic) disjoint union of {Xi}, then the coproduct topology (or...

{\textstyle \bigoplus _{n\geq 1}V^{\otimes n}} with the (non-cocommutative) coproduct Δ T c ¯ {\displaystyle \Delta _{\overline {T^{c}}}} given by splitting...

an atmosphere of fluorine. With hydrocarbons, hydrogen fluoride is a coproduct. It was first reported in 1926. It can also be prepared by the fluorination...

iron oxides. The Laux process is based on the finding that the oxide coproduct is strongly affected by various additives, such as ferrous chloride, aluminium...

equipped with a "tensor product" similar to multiplication in a ring, having coproducts similar to addition in a ring, in that the former is distributive over...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

News. November 13, 2017. Retrieved January 29, 2018. "Ammonia Plant: Coproduct yields agricultural benefit". Dakota Gasification Company. Retrieved July...

impurity in the synthesis of EDTA, arising from reactions of the ammonia coproduct. Older routes to NTA included alkylation of ammonia with chloroacetic...

algebras over a class of braided monoidal categories equipped with a coproduct and some notion of a gradation compatible with the braiding in the category...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

is not a complete category, but it is finitely complete. There is no coproduct in Met. The forgetful functor Met → Set assigns to each metric space the...

'coproduct.' Some studies leave it on the field to protect the soil from erosion and to add organic matter, while others take and burn the coproduct to...

"Effects of prepartum dietary cation-anion difference and acidified coproducts on dry matter intake, serum calcium, and performance of dairy cows". Journal...

requires a strong Brønsted base and a weak Lewis acid, and gives a methanol coproduct: (H2CO)2n + nB + nLA + nHArOH → nHC(=O)ArOH + n[HB][LA:OMe] Formally,...

direct sum ⨁ i ∈ I V i {\textstyle \bigoplus _{i\in I}V_{i}} (also called coproduct and denoted ∐ i ∈ I V i {\textstyle \coprod _{i\in I}V_{i}} ), where only...

𝜫 𝝅 𝝕 𝝥 𝝿 𝞏 𝞟 𝞹 𝟉 ℿ ℼ U+220F ∏ N-ARY PRODUCT, U+2210 ∐ N-ARY COPRODUCT Rho Ρ ρ Ῥ ῥ ῤ ϱ ϼ ᴩ ᵨ ☧ 𝚸 𝛒 𝛠 𝛲 𝜌 𝜚 𝜬 𝝆 𝝔 𝝦 𝞀 𝞎 𝞠 𝞺 𝟈 ⍴...

irrigation guidelines for farmers food safety use of waste biomass as coproducts with a goal to achieve zero waste use of solar energy during processing...

∗ b {\displaystyle a*b} be the coproduct of a {\displaystyle a} and b {\displaystyle b} . Note that the word coproduct is a diminutive of convolution...

object in the category of small categories. Given a category C with finite coproducts, a cogroup object is an object G of C together with a "comultiplication"...

proceeds via the bis(hydroperoxide) and the hydroquinone. Acetone is a coproduct. Another major process involves the direct hydroxylation of phenol by...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

multiplication. Isomorphism classes of objects in any distributive category, under coproduct and product operations, form a semiring known as a Burnside rig. A Burnside...

all epimorphisms) into surjections of sets (in the usual sense). The coproduct of two projective objects is projective. A retract of a projective object...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

category C with finite coproducts that are disjoint and well-behaved with respect to pullbacks. Equivalently, C is extensive if the coproduct functor from the...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

initial object is the empty set, with its trivial measurable structure; The coproduct is given by the disjoint union of measurable spaces, with its canonical...

vector space of the algebra, while the pair of pants gives a product or coproduct, depending on how the boundary components are grouped – which is commutative...

glycine and nitrilotriacetic acid; they arise from reactions of the ammonia coproduct. To describe EDTA and its various protonated forms, chemists distinguish...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

The process was once attractive because of the value of the hydrogen coproduct, but in modern times is not economically viable. The hydroformylation...

{\displaystyle B} in a category C {\displaystyle {\mathcal {C}}} where the coproducts B ⊔ B {\displaystyle B\sqcup B} exists, the codiagonal is the canonical...

point produces a totally disconnected space. Subspaces, products, and coproducts of totally disconnected spaces are totally disconnected. Totally disconnected...

. {\displaystyle 1\otimes v=1\cdot v=v.} With the usual product this coproduct does not make T(V) into a bialgebra, but is instead dual to the algebra...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

sets. Categorical constructions lead to some examples. For example, the coproduct of spaces is the disjoint union and thus corresponds to the direct sum...

peptide-C(O)NHCH(OH)CO2− → peptide-C(O)NH2 + CH(O)CO2− The eliminated coproduct is glyoxylate, written above as CH(O)CO2−. Insect PαAMs are responsive...

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ISOamsb n-ary product (product sign) ∐ ∐ ∐ U+2210 HTML 5.0 ISOamsb n-ary coproduct (coproduct sign) ∑ ∑ ∑ U+2211 HTML 4.0 HTML 5...

{\displaystyle \left(x_{0},y_{0}\right)} serving as the basepoint. The coproduct in the category of pointed spaces is the wedge sum, which can be thought...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

As an R-module, H is free with a basis 1 = D(0), D(1), D(2), ... The coproduct Δ is given by ΔD(n) = ΣD(i) ⊗ D(n−i) (so the dual of this coalgebra is...

y)\|_{\infty }=\max(\|x\|,\|y\|)} which correspond (respectively) to the coproduct and product in the category of Banach spaces and short maps (discussed...

unique set {hi ∈ Hi : i ∈ S} such that g = Π {hi : i in S}. Direct sum Coproduct Free product Direct sum of topological groups Homology. Saunders MacLane...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

by bounding logarithms. Similarly for the right-hand side the infinite coproduct of reals greater than one does not guarantee divergence, e.g., lim n →...

axiom (AB2). AB3 categories are abelian categories possessing arbitrary coproducts (hence, by the existence of quotients in abelian categories, also all...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

help with the shipping of "dry distillers grain with solubles" (DDGS), a coproduct of produced by the conversion of corn to ethanol, a significant bovine...

parameter with ISBN (link) Aso, Sammy N. (2020-05-11). Digestate: The Coproduct of Biofuel Production in a Circular Economy, and New Results for Cassava...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

any two nontrivial groups is infinite. The free product is actually the coproduct in the category of groups. If G and H are groups, a subdirect product...

k} , on the level of k {\displaystyle k} -points, the (set-theoretic) coproduct p k : ∐ α U α ( k ) → X ( k ) {\displaystyle p_{k}:\coprod _{\alpha }U_{\alpha...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

made into a commutative and cocommutative Hopf algebra as follows. The coproduct of Exp(G) is defined so that all the elements exp(gt) are group-like....

direct sum of vector spaces, which is both a categorical product and a coproduct, the tensor product, which makes FinVect a compact closed category. Tensor...

family of sets indexed by another set, one can form the disjoint union or coproduct ∐ i ∈ I A i {\displaystyle \coprod _{i\in I}A_{i}} , which is the set...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

where sodium chloride is electrolysed, sodium hydroxide and chlorine are coproducts. Industrially, there are three chloralkali processes: The Castner–Kellner...

published it in 1962. Suppose that: The functor F: Hotcop → Set maps coproducts (i.e. wedge sums) in Hotc to products in Set: F ( ∨ α X α ) ≅ ∏ α F (...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

is given by the shuffle product (a1,...,am) ш (m + b1,...,m + bn). The coproduct of a permutation a on m points is given by Σa=b*c st(b) ⊗ st(c), where...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

2-Octanol is produced commercially by base-cleavage of ricinoleic acid. The coproduct is a mixture of sebacic acid ((C8H16CO2H)2). Castor oil, which consists...

filtered homotopy colimits). For a triangulated category C which admits all coproducts, Neeman (2001a) defines an object to be compact if Hom C ⁡ ( X , ⋅ ) :...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

cocomplete. The empty assembly is initial and binary coproducts correspond to category-theoretic binary coproducts. Similarly to equalizers, the coequalizer of...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

R[b1, b2, ...], where R is the reduced bordism ring of a 0-sphere. The coproduct is given by ψ ( b k ) = ∑ i + j = k ( b ) 2 i j + 1 ⊗ b j {\displaystyle...

Meas is given by the product sigma-algebra on the Cartesian product. The coproduct is given by the disjoint union of measurable spaces. The equalizer of...

{Top} } is given by the product topology on the Cartesian product. The coproduct is given by the disjoint union of topological spaces. The equalizer of...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

2008. Nutritional properties and feeding values of soybeans and their coproducts. Soybeans chemistry, production, processing, and utilization. AOCS Press...

limit (or colimit) Fl. This can be applied to equalizers, products and coproducts among others. Applying it to kernels and cokernels, we see that the equivalence...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

{\displaystyle X+Y\rightarrow X*Y} through the universal property of the coproduct. One also has a canonical morphism X ∗ Y → Δ 0 ∗ Δ 0 ≅ Δ 1 {\displaystyle...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

benzene has been well investigated, motivated by the avoidance of HCl as a coproduct in the direct halogenation: 4 C6H6 + 4 HCl + O2 → 4 C6H5Cl + H2O This...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

crystal base ( L ′ , B ′ ) {\displaystyle (L',B')} . For crystal bases, the coproduct Δ {\displaystyle \Delta } , given by Δ ( k λ ) = k λ ⊗ k λ Δ ( e i ) =...

could be washed with cold water to remove the ammonium chloride ([NH4]Cl) coproduct. The new compound contained P, N, and Cl, on the basis of elemental analysis...

mathematics, a category is distributive if it has finite products and finite coproducts and such that for every choice of objects A , B , C {\displaystyle A,B...

x ∈ H {\displaystyle x\in H} , where Δ {\displaystyle \Delta } is the coproduct on H, and the linear map T : H ⊗ H → H ⊗ H {\displaystyle T:H\otimes H\to...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

gypsum, molybdenum, strontium, silica, uranium, and gold (most as a coproduct of the Sarcheshmeh copper complex operations). The mines at Sarcheshmeh...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

2008. Nutritional properties and feeding values of soybeans and their coproducts. Soybeans chemistry, production, processing, and utilization. AOCS Press...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

the tensor product become a fibered coproduct in the category of commutative R-algebras. (But it is not a coproduct in the category of R-algebras.) If...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Silva JC (June 2006). "Firefly luciferase produces hydrogen peroxide as a coproduct in dehydroluciferyl adenylate formation". ChemBioChem. 7 (6): 929–935...

B0(m, n) is a finite group. In terms of category theory, B0(m, n) is the coproduct of n cyclic groups of order m in the category of finite groups of exponent...

products and coproducts and form quotient objects within the given category. If one drops "extended", one can only take finite products and coproducts. If one...

identity operator. The total angular momentum operators are defined by the coproduct (or tensor product) of the two representations acting on V1⊗V2, J ≡ j...

unit/ source map η R : A → Γ  right unit/ target map Δ : Γ → Γ ⊗ A Γ  coproduct/ composition map ε : Γ → A  counit/ identity map  c : Γ → Γ  conjugation/...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

{\mathcal {A}}} , the edges in B {\displaystyle {\mathcal {B}}} . This is the coproduct. This can be defined in general for a family of coherent spaces, { A i...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

exists a faithful functor P : SetCop → Set which maps a presheaf X to the coproduct ∐ c ∈ o b C X ( c ) {\displaystyle \coprod _{c\in \mathrm {ob} C}X(c)}...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

production process whereas coproducts are intentionally produced. Byproducts need further processing to be useful whereas coproducts are highly processed and...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

union (rather than the cartesian product as it is in Set), and so is the coproduct. Rel is monoidal closed, if one defines both the monoidal product A ⊗...

give kG the structure of a cocommutative Hopf algebra by defining the coproduct, counit, and antipode to be the linear extensions of the following maps...

abelian if it has a zero object, it has all binary products and binary coproducts, and it has all kernels and cokernels. all monomorphisms and epimorphisms...

(C5H5)2Ti(SC6H5)2 + 2 CO Some metal centers are oxidized by thiols, the coproduct being hydrogen gas: Fe3(CO)12 + 2 C2H5SH → Fe2(SC2H5)2(CO)6 + Fe(CO)5...

show that A b {\displaystyle \mathbf {Ab} } is a complete category. The coproduct in A b {\displaystyle \mathbf {Ab} } is given by the direct sum; since...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

from A to B, this means that c(a1a2) = Σc1(a1)c2(a2) where Σc1⊗c2 is the coproduct of c, and c multiplies identities by the counit of c. In particular if...

into the hydroxylated product, and one oxygen atom into the succinate coproduct. Its interactions with HIF-1α rely on a mobile loop region that helps...

are any nucleophile, triphenylphosphine, and a diazodicarboxylate; the coproducts are triphenyl­phosphine oxide and a hydrazodiamide.[citation needed] Two...

consisting of arrows (morphisms) linking objects, such as products and coproducts. According to McLarty (2005), this diagrammatic approach to contemporary...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

other object in that category; it is initial. This serves to define the coproduct in C {\displaystyle {\mathcal {C}}} , when it exists. William Lawvere...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

anhydrous ammonia for simplicity: 6 S2Cl2 + 16 NH3 → S4N4 + S8 + 12 [NH4]Cl Coproducts of this reaction include heptasulfur imide (S7NH) and elemental sulfur;...

greenhouse gas emissions compared to fossil derived ethylene, due to coproduct credits and carbon capture. The study also examined coprocessing ethanol...

donates the equivalent of α-amino-γ-butyrolactone. Methylthioadenosine is a coproduct. Homoserine lactones are also a product of the proteolytic reaction of...

generated over k by c and x with the relations cn=1, xn=0, xc=ζcx. The coproduct takes c to c⊗c and x to c⊗x + x⊗1. The counit takes c to 1 and x to 0...

{\displaystyle R_{j}} the rotations and N j {\displaystyle N_{j}} the boosts. The coproducts are: Δ P j = P j ⊗ 1 + e − λ P 0 ⊗ P j   , Δ P 0 = P 0 ⊗ 1 + 1 ⊗ P 0 {\displaystyle...

X_{\alpha }} itself, such that any object X is the direct sum (i.e., coproduct or, equivalently, product) of finitely many simple objects. It follows...

their selectivities can be high, limiting the coproduction of undesirable coproducts. Generally operating under mild temperatures and pressures in aqueous...

manner similar to the free product of groups. The free product is the coproduct in the category of R-algebras. Tensor products The tensor product of two...

contain a 1 in the i-th slot and zeros elsewhere. This vector space is the coproduct (or direct sum) of countably many copies of the vector space F. Note the...

structure constants of the Hall algebra. In addition to the product, the coproduct and the antipode of a Hopf algebra can be expressed in terms of structure...

Scotland, June 2001. Birkhäuser. pp. 77–92. Tamanoi, Hirotaka (2010). "Loop coproducts in string topology and triviality of higher genus TQFT operations". Journal...

is the categorical product and the additive monoidal structure is the coproduct are called distributive categories. Vect, the category of vector spaces...

267–297, doi:10.1016/0021-8693(76)90160-5 Bergman, George M. (1974), "Coproducts and some universal ring constructions", Transactions of the American Mathematical...

\Pi _{2}} is given by the preceding formula. For quantum groups, the coproduct is no longer co-commutative. As a result, the natural permutation map...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

skeletal muscle functions anaerobically, generating lactate and ammonia a coproduct of muscle myoadenylate deaminase (AMPD) activity. The forearm ischemic...

contact with a hot surface, releasing the hydrocarbon ligands as gaseous coproducts. This process has been considered as a means of preparing nickel films...

Engineers 2008 – MycoMax fungal process for additional ethanol plant coproduct, R&D 100 Awards, R&D Magazine 2008 – Fungal process for ethanol plant...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

ring Z⟨Z1, Z2,...⟩ generated by non-commuting variables Z1, Z2, ... The coproduct takes Zn to Σ Zi ⊗ Zn–i, where Z0 = 1 is the identity. The counit takes...

it represents (the global-section functor) preserves epimorphisms and coproducts. There are several relationship between the five properties discussed...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

Manjusri; Mohanty, Amar K. (22 July 2016). "Characterization of Wastes and Coproducts from the Coffee Industry for Composite Material Production". BioResources...

map Δ : f ↦ f [ X + Y ] {\displaystyle \Delta :f\mapsto f[X+Y]} is the coproduct for the Hopf algebra structure on the ring of symmetric functions. h n...

new finite list with the number at the head. In categories with binary coproducts, the definitions just given are equivalent to the usual definitions of...

category of presheaves SetCop is equivalent to the exact completion of the coproduct completion of C. The effective topos is the exact completion of the category...

Because extension of scalars is base change, it preserves limits and coproducts. This implies in particular that if X has an algebraic structure defined...

an exact functor F : D → T {\displaystyle F\colon D\to T} sends coproducts to coproducts, then F has a right adjoint. The Brown representability theorem...

Lie algebras, which allows us to define some operations analogous to coproducts, counits and antipodes of Hopf algebras. Since the Vassiliev invariants...

low oxygen conditions (pyrolysis). The process produces biochar as a coproduct, which can be substituted in any application that uses coal, or used as...

B.D.; Dale, B.E.; Allen, M.S. (February 2011). "Grass leaf protein, a coproduct of cellulosic ethanol production, as a source of protein for livestock"...

Botswana and Zimbabwe. The majority of South Africa's nickel output was a coproduct of platinum metals group mining. Higher South African production was partially...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

replace animal manures by fertilizers and to replace also other animal coproducts, and because livestock now use human-inedible food and fiber processing...

11.2829. MR 2846913. S2CID 58893087. Tamanoi, Hirotaka (2010). "Loop coproducts in string topology and triviality of higher genus TQFT operations". Journal...

being quantitative like metric spaces. One can take arbitrary products, coproducts, and quotients, and the results appropriately generalize the corresponding...

and only if C {\displaystyle {\mathcal {C}}} is closed under arbitrary coproducts (a.k.a. direct sums). Hence the notion of a localizing subcategory is...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

above, this is special (in this case, it is because all sets are iterated coproducts of {1}). Barr, Michael; Wells, Charles (1985). Toposes, Triples and Theories...

the wedge product X ∧ Y {\displaystyle X\wedge Y} of X and Y is the coproduct of X and Y; concretely, it is obtained by taking their disjoint union...

groups etc.) vs. submodules, direct products vs. direct sums (also called coproducts to emphasize the duality aspect). Therefore, in some cases, proofs of...

will be recovered from somewhat uncommon rocks, there will be much more coproducts and byproducts from a given operation, and more trade in minerals and...

universal properties, and the isomorphism between finite products and coproducts, we have the character groups of G {\displaystyle G} is isomorphic to...

H^{i}(X,-):{\text{Ab}}(X)\to {\text{Ab}}} preserve direct limits and coproducts. Given a locally finite type morphism f : X → S {\displaystyle f:X\to...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

2,2-Dibromo-3-Nitrilopropionamide (DBNPA) in Bioethanol Fermentation Coproducts". World Journal of Microbiology and Biotechnology. 38 (5): 82. doi:10...

Hopf algebra over a field k. Let Δ {\displaystyle \Delta } denote the coproduct and S the antipode of H. Let V be a vector space over k. Then V is called...

{\displaystyle C^{\perp \ell }} is closed under retracts, pushouts, (small) coproducts & transfinite composition (filtered colimits) of morphisms (whenever they...

manufacturing process of lactylates is an esterification reaction. The water coproduct is removed by evaporation to drive the reaction towards the desired product...

generated by elements x,y, 1/y, with the relations xy + yx = x2 = 0. The coproduct takes x to x⊗1 + (1/y)⊗x and y to y⊗y, and the counit takes x to 0 and...

\right)\left({\begin{array}{c}\sinh \tau \\\cosh \tau \end{array}}\right)} The coproducts are classical, and encode the group composition law: Δ a μ = Λ μ ν ⊗ a...

Stakeholders, the Iowa Power Fund Board, and the Renewable Fuels and Coproducts Advisory Committee. *incumbent "Canvass Summary - Final - 2004 General...

The fundamental group functor takes products to products and coproducts to coproducts. That is, if X {\displaystyle X} and Y {\displaystyle Y} are path...

functors from extremally disconnected profinite sets to sets sending finite coproducts to products. Compactification (mathematics) – Embedding a topological...

which could be caused by the absence of acetone or acetaldehyde as a coproduct, which lead to reduced enzyme activities. Kara S, Spickermann D, Schrittwieser...

Iowa. OCLC 26693781. Knox, Nathaniel (1974). On the inverse semigroup coproduct of an arbitrary non-empty collection of groups. Columbia, SC: University...

Products Equalizers Kernels Pullbacks Inverse limit Colimits Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit Algebraic categories...

{\displaystyle M\oplus N} . In the category of vector spaces, finite products and coproducts coincide: algebraically, M ⊕ N {\displaystyle M\oplus N} and M × N {\displaystyle...

higher-order fibration over the category Set for which the products and coproducts induced by functions satisfy the Beck-Chevalley condition. This disambiguation...

to denote lists over A. In a category with a terminal object 1, binary coproducts (denoted by +), and binary products (denoted by ×), a list object over...

∞-category has all small limits if and only if it has coequalizers and small coproducts. If a functor admits a left adjoint, then it commutes with all limits...

language features they require. Multiple dispatch Ruby syntax § Open classes Coproducts of functors JavaGI type classes Tagless-final / Object algebras Polymorphic...

V\in {}_{H}^{H}{\mathcal {YD}}} is always a Braided Hopf algebra. The coproduct Δ {\displaystyle \Delta } and counit ϵ {\displaystyle \epsilon } of T...

deposit is mined again, Fluorite and vonsenite should be considered as coproducts. Because of the magnetic properties of the ore in Jayville, new technologies...

Desuspension makes the category of spaces a triangulated category. If arbitrary coproducts were allowed, desuspension would result in all cohomology functors being...

sequences, an equivalent characterization of excision. It preserves arbitrary coproducts. This reflects the disjoint-union axiom of h ∗ {\displaystyle h_{*}} ...

adhesive category and HLR system are related (an adhesive category with coproducts is a HLR system). Hypergraph, typed graph and attributed graph rewriting...