Subject: categories: Reading advise on bicategory theory

From: Lars Lindqvist <[email-masked]>
Date: Sat, 30 Jan 1999 11:48:10 +0100 (MET)

Hi,

I am looking for advise on suitable litterature for a beginner in
bicategory-theory. The litterature I have found so far is:

Kelly, Street  Review of the elements of 2-categories
Borceux        Handbook of categorical algebra 1

I have also ordered the following article:

Benabou        Introduction to bicategories

So far I have only read Borceux's book but it contains mainly
definitions. In particular I have difficulties understanding
the need for (and consequences of) the coherence axioms
associated with the natural isomorphisms expressing the
associativity and identity 'axioms'.

/Lars Lindqvist

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From: John R Isbell <[email-masked]>
Date: Sun, 31 Jan 1999 10:20:19 -0500 (EST)

Lars, I would guess that you will get more advice than you can
use. Here is my nickel's worth. 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.

   _____________________________
   John R. Isbell
   [email-masked] or [email-masked]
   Homepage: www.unipissing.ca/topology/z/a/a/a/05.htm
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