Reading advise on bicategory theory
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
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 ji2@buffalo.edu or ji2@acsu.buffalo.edu Homepage: www.unipissing.ca/topology/z/a/a/a/05.htm _________________________________________________ | | | Der Mensch ist nur da ganz Mensch, wo er spielt. | | | | -- Friedrich Schiller | |_________________________________________________ | On Sat, 30 Jan 1999, Lars Lindqvist wrote:
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
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.
participants (3)
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james dolan -
John R Isbell -
Lars Lindqvist