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.
Publié le : 2006-03-14
Classification:
monoidal categories,
symmetric monoidal categories,
coherence,
Mac Lane’s pentagon,
Mac Lane’s hexagon,
insertion,
18D10,
18A05
@article{1140641170,
author = {Do\v sen, Kosta and Petr\'c, Zoran},
title = {Associativity as commutativity},
journal = {J. Symbolic Logic},
volume = {71},
number = {1},
year = {2006},
pages = { 217-226},
language = {en},
url = {http://dml.mathdoc.fr/item/1140641170}
}
Došen, Kosta; Petrć, Zoran. Associativity as commutativity. J. Symbolic Logic, Tome 71 (2006) no. 1, pp. 217-226. http://gdmltest.u-ga.fr/item/1140641170/