In their paper "Strong stacks and classifying spaces" A. Joyal and M. Tierney provide an internal characterization of the "classical" (or "folk") model structure on the category of groupoids in a Grothendieck topos E. The fibrant objects in the classical model structure on Gpd(E) are called "strong stacks", and they appear as a strengthening of the notion of "stack in E" (i.e. an internal groupoid object in E subject to a certain condition). The main application (almost untouched in this presentation) is when E is the topos of simplicial sheaves on a space or on a site, then strong stacks are intimately connected with classifying spaces of simplicial groups. The aim of my presentation is to give a precise account of the technicalities which allow to understand Joyal&Tierney's result: the first lecture will be about the fundamentals of Topos Theory and a brief introduction to the theory of Model Categories.

## Homotopical interpretation of stacks

Research Group:

Fosco Loregian

Institution:

SISSA

Schedule:

Tuesday, April 23, 2013 - 16:00 to 17:30

Location:

A-136

Abstract: