RE: query

["Noson S. Yanofsky" <noson@sci.brooklyn.cuny.edu>]

> -----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




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