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Associativity as commutativity

Published online by Cambridge University Press:  12 March 2014

Kosta Dǒsen  and
Zoran Petrić
Kosta Dǒsen
Affiliation:
Mathematical Institute, Sanu, Knez Mihailova 35, P.F. 367, 11001 Belgrade, Serbia. E-mail: kosta@mi.sanu.ac.yu
Zoran Petrić
Affiliation:
Mathematical Institute, Sanu, Knez Mihailova 35, P.F. 367, 11001 Belgrade, Serbia. E-mail: zpetric@mi.sanu.ac.yu
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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.

Keywords

monoidal categoriessymmetric monoidal categoriescoherenceMac Lane's pentagonMac Lane's hexagoninsertion
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 1 , March 2006 , pp. 217 - 226
Copyright
Copyright © Association for Symbolic Logic 2006

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References

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