Re: query

Dear Jim, On Wed, 24 Jun 2009, jim stasheff wrote:

Mac Lane coherence can be deduced from the simple connectivity of the associahedron

Surely that's not true, assuming that by "Mac Lane coherence" you mean Mac Lane's coherence theorem for monoidal categories. The associahedra (and in particular the pentagon) say nothing about the unit coherence isomorphisms, X \otimes I ----> X <---- I \otimes X. To make it true, surely you need to weaken Mac Lane's theorem to a statement about "semigroupal" categories, i.e. monoidal categories without unit...? Best wishes, Tom [For admin and other information see: http://www.mta.ca/~cat-dist/ ]