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Classifying Spaces for Monoidal Categories Through Geometric Nerves

  Published:2004-09-01
 Printed: Sep 2004
  • M. Bullejos
  • A. M. Cegarra
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Abstract

The usual constructions of classifying spaces for monoidal categories produce 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: monoidal category, pseudo-simplicial category, simplicial set, classifying space, homotopy type monoidal category, pseudo-simplicial category, simplicial set, classifying space, homotopy type
MSC Classifications: 18D10, 18G30, 55P15, 55P35, 55U40 show english descriptions Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23]
Simplicial sets, simplicial objects (in a category) [See also 55U10]
Classification of homotopy type
Loop spaces
Topological categories, foundations of homotopy theory
18D10 - Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23]
18G30 - Simplicial sets, simplicial objects (in a category) [See also 55U10]
55P15 - Classification of homotopy type
55P35 - Loop spaces
55U40 - Topological categories, foundations of homotopy theory
 

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