-----Original Message----- From: categories@mta.ca [mailto:categories@mta.ca] On Behalf Of jim stasheff Sent: Wednesday, June 24, 2009 12:18 PM To: Categories list Subject: categories: query
Mac Lane coherence can be deduced from the simple connectivity of the associahedron Is it written that way anywhere?
jim
Hi, Yes. My thesis. "Obstructions to Coherence: Natural Noncoherent Associativity and Tensor Functors", City University of New York, 1996. The part about the associahedron was published in Obstructions to Coherence: Noncoherent Associativity The Journal of Pure & Applied Algebra. 147 no. 2, Pgs 175 - 213. (2000). or http://xxx.lanl.gov/abs/math.QA/9804106 The second part about the tensor functors was never published. I look at the fundamental group of the associahedra thought of as groupoids (called the "Catalan groupoids"). They are all trivial. But then I ask, what if the pentagons do not commute? The fundamental group of the Mac Lane non-commuting pentagon is Z. And I get generators and relations for all the higher non-commuting associahedra. They are not free groups from n=7 on. I do a similar thing for non-coherent tensor functors (monoidal functors). All the best, Noson [For admin and other information see: http://www.mta.ca/~cat-dist/ ]