Authors: Došen, Kosta 
Petrić, Zoran 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Associativity as commutativity
Journal: Journal of Symbolic Logic
Volume: 71
Issue: 1
First page: 217
Last page: 226
Issue Date: 1-Jan-2006
Rank: M22
ISSN: 0022-4812
DOI: 10.2178/jsl/1140641170
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.
Keywords: Coherence | Insertion | Mac Lane's hexagon | Mac Lane's pentagon | Monoidal categories | Symmetric monoidal categories
Publisher: Association for Symbolic Logic

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