Associativity as Commutativity

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dc.creatorDosen, K.
dc.creatorPetric, Z.
dc.date2005-06-29
dc.date2007-05-18
dc.date.accessioned2026-07-07T08:02:07Z
dc.date.available2026-07-07T08:02:07Z
dc.descriptionIt 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.
dc.description15 pages, braiding mentioned, minor corrections, references updated
dc.identifierhttps://arxiv.org/abs/math/0506600
dc.identifierhttp://arxiv.org/abs/math/0506600
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/129128
dc.subjectCategory Theory
dc.subjectLogic
dc.subject18D10; 18A05
dc.titleAssociativity as Commutativity
dc.typetext

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