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Classifying Spaces for Monoidal Categories Through Geometric Nerves

Published online by Cambridge University Press:  20 November 2018

M. Bullejos  and
A. M. Cegarra
M. Bullejos
Affiliation:
Departamento de Álgebra Facultad de Ciencias Universidad de Granada 18071 Granada, Spain, bullejos@ugr.es
A. M. Cegarra
Affiliation:
Departamento de Álgebra Facultad de Ciencias Universidad de Granada 18071 Granada, Spain, cegarra@ugr.es
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Abstract

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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.

Keywords

18D1018G3055P1555P3555U40monoidal categorypseudo-simplicial categorysimplicial setclassifying spacehomotopy type
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 3 , 01 September 2004 , pp. 321 - 331
Copyright
Copyright © Canadian Mathematical Society 2004

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