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Classifying Spaces for Monoidal Categories Through Geometric Nerves |
Published:2004-09-01
Printed: Sep 2004
Printed: Sep 2004
- M. Bullejos
- A. M. Cegarra
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 |
| MSC Classifications: |
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 |