Equivalence relations

[David Roberts <droberts@maths.adelaide.edu.au>]

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

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