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March 2006 Associativity as commutativity
Kosta Došen, Zoran Petrć
J. Symbolic Logic 71(1): 217-226 (March 2006). DOI: 10.2178/jsl/1140641170

Abstract

It is shown that coherence conditions for monoidal categories concerning associativity are analogous to coherence conditions for symmetric 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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Kosta Došen. Zoran Petrć. "Associativity as commutativity." J. Symbolic Logic 71 (1) 217 - 226, March 2006. https://doi.org/10.2178/jsl/1140641170

Information

Published: March 2006
First available in Project Euclid: 22 February 2006

zbMATH: 1099.18006
MathSciNet: MR2210063
Digital Object Identifier: 10.2178/jsl/1140641170

Subjects:
Primary: 18A05, 18D10

Rights: Copyright © 2006 Association for Symbolic Logic

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Vol.71 • No. 1 • March 2006
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