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Classifying Spaces for Monoidal Categories Through Geometric Nerves

Published online by Cambridge University Press:  20 November 2018

M. Bullejos
Departamento de Álgebra Facultad de Ciencias Universidad de Granada 18071 Granada, Spain,
A. M. Cegarra
Departamento de Álgebra Facultad de Ciencias Universidad de Granada 18071 Granada, Spain,
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The usual constructions of classifying spaces for monoidal categories produce $\text{CW}$-complexes with many cells that,moreover, do not have any proper geometric meaning. However, geometric nerves of monoidal 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.

Research Article
Copyright © Canadian Mathematical Society 2004


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