Subject: Vogt's answer to Stasheff
Date: Sat, 18 Oct 2003 10:27:04 -0500 (CDT)
From: Peter May <may@math.uchicago.edu>
To: dmd1@lehigh.edu

Right. The comparison among categories, Segal categories, and
A_{\infty} categories works just like the comparison (Thomason,
Fiedorowicz) among topological monoids, Segal \Delta spaces,
and A_{\infty} spaces.  This will be in a paper I'm writing,
where analogous comparisons for n-categories are studied ---
there one can compare Segalic and A_{\infty} approaches, but
the two give versions of weak n-categories that, in contrast to
the category case, cannot be equivalent to strict n-categories.

Peter May