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- catalog abstract "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.".
- catalog contributor b8696931.
- catalog created "1995.".
- catalog date "1995".
- catalog date "1995.".
- catalog dateCopyrighted "1995.".
- catalog description "Basic definitions -- First examples -- Some constructions of topoi -- Cohomology and homotopy -- Group actions -- Diaconescu's theorem -- The classifying topos of a topological category -- Diaconescu's theorem for s-etale categories -- Sheaves on simplicial spaces -- Cohomology of classifying topoi -- Some homotopy equivalences between classifying topoi -- Geometric realization of simplicial spaces -- Classifying spaces -- Geometric realization by cosimplicial topoi -- Sheaves and geometric realization -- Discrete categories -- s-Etale categories -- Segal's theorem on [Gamma][superscript q] -- Comparison for topological categories.".
- catalog description "Includes bibliographical references (p. - ) and index.".
- catalog description "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.".
- catalog extent "94 p.".
- catalog hasFormat "Classifying spaces and classifying topoi.".
- catalog identifier "3540603190 (pbk. : acid-free paper)".
- catalog isFormatOf "Classifying spaces and classifying topoi.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1616.".
- catalog isPartOf "Lecture notes in mathematics ; 1616".
- catalog issued "1995".
- catalog issued "1995.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog relation "Classifying spaces and classifying topoi.".
- catalog subject "510 s 514/.24 20".
- catalog subject "Algebraic topology.".
- catalog subject "Classifying spaces.".
- catalog subject "Grothendieck categories.".
- catalog subject "K-theory.".
- catalog subject "Mathematics.".
- catalog subject "QA3 .L28 no. 1616 QA612.7".
- catalog subject "Toposes.".
- catalog tableOfContents "Basic definitions -- First examples -- Some constructions of topoi -- Cohomology and homotopy -- Group actions -- Diaconescu's theorem -- The classifying topos of a topological category -- Diaconescu's theorem for s-etale categories -- Sheaves on simplicial spaces -- Cohomology of classifying topoi -- Some homotopy equivalences between classifying topoi -- Geometric realization of simplicial spaces -- Classifying spaces -- Geometric realization by cosimplicial topoi -- Sheaves and geometric realization -- Discrete categories -- s-Etale categories -- Segal's theorem on [Gamma][superscript q] -- Comparison for topological categories.".
- catalog title "Classifying spaces and classifying topoi / Izak Moerdijk.".
- catalog type "text".