Classifying Spaces and Classifying Topoi [electronic resource] / by Izak Moerdijk.
Material type: TextSeries: Lecture Notes in Mathematics ; 1616Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 1995Description: X, 98 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540449126Subject(s): Mathematics | K-theory | Algebraic topology | Mathematics | K-Theory | Algebraic TopologyAdditional physical formats: Printed edition:: No titleDDC classification: 512.66 LOC classification: QA612.33Online resources: Click here to access onlineCurrent library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available | EBK1290 |
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.
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