Classifying Spaces for Monoidal Categories Through Geometric Nerves

Abstract

AbstractThe usual constructions of classifying spaces for monoidal categories produce CW-complexes withmany cells that,moreover, do not have any proper geometricmeaning. However, geometric nerves ofmonoidal categories are very handy simplicial sets whose simplices have a pleasing geometric description: they are diagrams with the shape of the 2-skeleton of oriented standard simplices. The purpose of this paper is to prove that geometric realizations of geometric nerves are classifying spaces for monoidal categories.