Classifying Spaces and Classifying Topoi

Izak Moerdijk (auth.)3540603190, 9783540603191

This monograph presents a new, systematic treatment of the relation between classifying topoi and classifying spaces of topological categories. Using a new generalized geometric realization which applies to topoi, a weak homotopy equival- ence is constructed between the classifying space and the classifying topos of any small (topological) category. Topos theory is then applied to give an answer to the question of what structures are classified by “classifying” spaces.
The monograph should be accessible to anyone with basic knowledge of algebraic topology, sheaf theory, and a little topos theory.

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Table of contents :
Introduction….Pages 1-4
Background in topos theory….Pages 5-19
Classifying topoi….Pages 21-55
Geometric realization….Pages 57-76
Comparison theorems….Pages 77-88
Classifying spaces and classifying topoi….Pages 95-95