Dear all, Considering the well known fact that an equivalence relation R on a set S gives a groupoid S_R with object set S, and the quotient of S by R is pi_0(S_R), has anyone done any work on "equivalence relations" on categories? Taking the skeleton of a cat is the prototypical example, but what I had in mind was a more "relative" construction. Given a groupoid enriched in categories, taking a sort of Pi_1 would give us a groupoid mod "equivalent morphisms". There is a smell of relative homotopy about, and I don't know enough in that area. I realise there are a couple of levels to this game, as evidenced by Kapranov and Voevodsky in their paper on 2-cats and the Zamolodchikov tetrahedron equations - do we take a "skeleton" at one or more dimensions? Any pointers appreciated ------------------------------------------------------------------------ -- David Roberts School of Mathematical Sciences University of Adelaide SA 5005 ------------------------------------------------------------------------ -- droberts@maths.adelaide.edu.au www.maths.adelaide.edu.au/~droberts www.trf.org.au "Go ye into all the world, and preach the gospel to every creature." - Mark 16:15 CRICOS Provider Number 00123M ----------------------------------------------------------- This email message is intended only for the addressee(s) and contains information that may be confidential and/or copyright. If you are not the intended recipient please notify the sender by reply email and immediately delete this email. Use, disclosure or reproduction of this email by anyone other than the intended recipient(s) is strictly prohibited. No representation is made that this email or any attachments are free of viruses. Virus scanning is recommended and is the responsibility of the recipient.