Associativity as Commutativity

Details Associativity as Commutativity Associativity as Commutativity

2005-06-29

arxiv.org/abs/math/0506600v14

Mathematics

Category Theory

15 pages, braiding mentioned, minor corrections, references updated

Scientific paper

It is shown that coherence conditions for monoidal categories concerning associativity are analogous to coherence conditions for symmetric or braided strictly monoidal categories, where associativity arrows are identities. Mac Lane's pentagonal coherence condition for associativity is decomposed into conditions concerning commutativity, among which we have a condition analogous to naturality and a degenerate case of Mac Lane's hexagonal condition for commutativity. This decomposition is analogous to the derivation of the Yang-Baxter equation from Mac Lane's hexagon and the naturality of commutativity. The pentagon is reduced to an inductive definition of a kind of commutativity.

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