Title: Twisted Diagrams
Authors: Thomas Huettemann and Oliver Roendigs
AMS subject clssification (200): 55U35
Author addresses:
Thomas Huettemann
Department of Mathematical Sciences
King's College, University of Aberdeen
Aberdeen AB24 3FX
UK
Oliver Roendigs
Fakultaet fuer Mathematik
Universitaet Bielefeld
Postfach 10 01 31
D-33501 Bielefeld
Germany
Email: huette@maths.abdn.ac.uk (T. Huettemann)
oroendig@mathematik.uni-bielefeld.de (O. Roendigs)
File: twisted.ps
Abstract:
Twisted diagrams are generalised diagrams: the vertices are
allowed to live in different categories, and the structure
maps act through specified "twisting" functors between these
categories. Examples include spectra (in the sense of homotopy
theory) and quasi-coherent sheaves of modules on an algebraic
variety. We construct a twisted version of Kan extensions and
establish various model category structures (with pointwise
weak equivalences). Using these, we propose a definition of
``homotopy sheaves'' and show that a twisted diagram is a
homotopy sheaf if and only if it gives rise to a ``sheaf in
the homotopy category''.