Mathematics

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 space​s 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.