2009/01/21 by Johannes Ebert, Ebert, Johannes
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.0901.3295
The notion of the homotopy type of a topological stack has been around in the literature for some time. The basic idea is that an atlas X → \mathfrakX of a stack determines a topological groupoid \mathbbX with object space X. The homotopy type of \mathfrakX should be the classifying space B \mathbbX. The choice of an atlas is not part of the data of a stack and hence it is not immediately clear why this construction of a homotopy type is well-defined, let alone functorial. The purpose of this note is to give an elementary construction of such a homotopy-type functor.