I am interested in fibrations of categories.Being a homotopy theoreticist I got acquainted with this subject through Ronnie BROWN's paper on fibrations of groupoids (1970). Can anyone help me to find recent papers on this subject ? Thanks for the trouble. Rudger Kieboom (Brussels). ==============================================================================
I am interested in fibrations of categories.Being a homotopy theoreticist I got acquainted with this subject through Ronnie BROWN's paper on fibrations of groupoids (1970). Can anyone help me to find recent papers on this subject ? Thanks for the trouble.
Rudger Kieboom (Brussels).
The paper by P. J. Higgins and myself, "Fibrations and quotients of differentiable groupoids", J. London Math. Soc.(2) {\bf 42} (1990) 101--110. characterizes fibrations in Brown's sense in terms of the congruences they determine, and shows that a 'First Isomorphism Theorem' can be given for fibrations provided one extends the notion of normal subgroupoid. This paper is written in differentiable terms, but (as far as we know) the results were new also for the underlying algebra. They can be regarded as a kind of descent construction. Kirill Mackenzie ==============================================================================
Date: Wed, 18 Nov 1992 05:45:50 -0500 From: rkieboom@tena2.vub.ac.be (Rudger Kieboom)
I am interested in fibrations of categories.Being a homotopy theoreticist I got acquainted with this subject through Ronnie BROWN's paper on fibrations of groupoids (1970). Can anyone help me to find recent papers on this subject ? Thanks for the trouble.
Rudger Kieboom (Brussels).
This may be a little outside your realm of interest, but it is very recent. Du\u{s}ko Pavlovi\'{c}'s thesis, "Predicates and Fibrations" includes a nice chapter on fibrations as variable categories. From the introduction to that chapter: ... The theory of fibrations, or fibered categories, is just category theory relative to a bse category. Ordinary categories can be viewed as fibered over 1. ==============================================================================
participants (3)
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Kirill Mackenzie -
piggy@hilbert.maths.utas.edu.au -
rkieboom@tena2.vub.ac.be