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＜E-Book＞
Classifying Spaces and Classifying Topoi / by Izak Moerdijk
(Lecture Notes in Mathematics. ISSN:16179692 ; 1616)

Edition	1st ed. 1995.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	1995
Size	X, 98 p : online resource
Authors	*Moerdijk, Izak author SpringerLink (Online service)
Subjects	LCSH:K-theory LCSH:Algebraic topology FREE:K-Theory FREE:Algebraic Topology
Notes	Background in topos theory -- Classifying topoi -- Geometric realization -- Comparison theorems -- Classifying spaces and classifying topoi 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 HTTP:URL=https://doi.org/10.1007/BFb0094441

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