Subject: categories: Re: Reading advise on bicategory theory

From: james dolan <[email-masked]>
Date: Sun, 31 Jan 1999 17:28:51 -0800 (PST)

john isbell writes:

-The matter of coherence is wide open. There is a paper of Yanofsky
-accepted for publication in JPAA which investigates higher dimensional
-categories with no coherence assumptions at all -- this coming after a
-lot of work on weakened coherence. Benabou's basic point was that
-naturally arising 2-dimensional categories are not quite 2-categories
-and don't seem to suffer from it. Avoid getting knotted in coherence
-questions, especially in 1999.

what does "no coherence assumptions at all" mean in this context?
does it mean that yanofsky is studying what i call "coarse
n-categories", defined recursively as categories enriched over the
cartesian closed category where the objects are the coarse
[n-1]-categories and the morphisms are the enriched natural
isomorphism classes of enriched functors?  coarse n-categories are
interesting but they're obviously not the whole story; for example
it's straightforward to define the "fundamental coarse n-groupoid" of
a space, but it's indeed a rather coarse invariant of the homotopy
type.