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Classifying Spaces for Monoidal Categories Through Geometric Nerves
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 2004
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