Classifying Spaces and Classifying Topoi: 1616 (Lecture Notes in Mathematics, 1616) - Softcover

Moerdijk, Izak

Softcover

ISBN 10: 3540603190 ISBN 13: 9783540603191

Publisher: Springer, 1995

Synopsis

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.

About this title

Synopsis

This monograph presents a treatment of the relation between classifying topoi and classifying spaces of topological categories. Using a generalized geometric realization which applies to topoi, a weak homotopy equivalence 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.

Edition details

• Publisher: Springer
• Publication date: 1995
• Language: English
• ISBN 10: 3540603190
• ISBN 13: 9783540603191
• Binding: Paperback
• Number of pages: 108