. C T ] 2 9 Ju n 20 05 Associativity as Commutativity

It is shown that coherence conditions for monoidal categories concerning associativity are analogous to coherence conditions for strict symmetric 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. The pentagon is reduced to an inductive definition of a kind of commutativity. Mathematics Subject Classification (2000): 18D10, 18A05