Classifying Spaces and Classifying Topoi
Moerdijk, Izak.
Classifying Spaces and Classifying Topoi [electronic resource] / by Izak Moerdijk. - X, 98 p. online resource. - Lecture Notes in Mathematics, 1616 0075-8434 ; . - Lecture Notes in Mathematics, 1616 .
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.
9783540449126
10.1007/BFb0094441 doi
K-theory.
Algebraic topology.
K-Theory.
Algebraic Topology.
QA612.33
512.66
Classifying Spaces and Classifying Topoi [electronic resource] / by Izak Moerdijk. - X, 98 p. online resource. - Lecture Notes in Mathematics, 1616 0075-8434 ; . - Lecture Notes in Mathematics, 1616 .
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.
9783540449126
10.1007/BFb0094441 doi
K-theory.
Algebraic topology.
K-Theory.
Algebraic Topology.
QA612.33
512.66