Decomposing the classifying diagram in terms of classifying spaces of groups

Abstract

The classifying diagram was defined by Rezk and is a generalization of the nerve of a category; in contrast to the nerve, the classifying diagram of two categories is equivalent if and only if the categories are equivalent. In this paper we prove that the classifying diagram of any category is characterized in terms of classifying spaces of stabilizers of groups. We also prove explicit decompositions of the classifying diagrams for the categories of finite ordered sets, finite dimensional vector spaces, and finite sets in terms of classifying spaces of groups