Associativity isomorphism

In mathematics, specifically in the field of category theory, the associativity isomorphism implements the notion of associativity with respect to monoidal products in semi-groupal (or monoidal-without-unit) categories. == Definition == A category, C {\displaystyle {\mathcal {C}}} , is called semi-groupal if it comes equipped with a functor C × C → C {\displaystyle {\mathcal {C}}\times {\mathcal {C}}\to {\mathcal {C}}} such that the pair ( A , B ) ↦ A ⊗ B {\displaystyle (A,B)\mapsto A\otimes B} for A , B ∈ ob ( C ) {\displaystyle A,B\in {\text{ob}}({\mathcal {C}})} , as well as a collection of natural isomorphisms known as the associativity isomorphisms (or "associators").

Source: Wikipedia — Associativity isomorphism (CC BY-SA 4.0)

Associativity isomorphism

In mathematics, specifically in the field of category theory, the associativity isomorphism implements the notion of associativity with respect to monoidal products in semi-groupal (or monoidal-without-unit) categories. == Definition == A category, C {\displaystyle {\mathcal {C}}} , is called semi-groupal if it comes equipped with a functor C × C → C {\displaystyle {\mathcal {C}}\times {\mathcal {C}}\to {\mathcal {C}}} such that the pair ( A , B ) ↦ A ⊗ B {\displaystyle (A,B)\mapsto A\otimes B} for A , B ∈ ob ( C ) {\displaystyle A,B\in {\text{ob}}({\mathcal {C}})} , as well as a collection of natural isomorphisms known as the associativity isomorphisms (or "associators").

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Source: Wikipedia "Associativity isomorphism" · CC BY-SA 4.0

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