Geodesic
Classifying Spaces for Monoidal Categories Through Geometric Nerves
Canadian mathematical bulletin, Tome 47 (2004) no. 3, pp. 321-331

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DOI

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.
DOI : 10.4153/CMB-2004-031-8
Mots-clés : 18D10, 18G30, 55P15, 55P35, 55U40, monoidal category, pseudo-simplicial category, simplicial set, classifying space, homotopy type 
Bullejos, M.; Cegarra, A. M. Classifying Spaces for Monoidal Categories Through Geometric Nerves. Canadian mathematical bulletin, Tome 47 (2004) no. 3, pp. 321-331. doi: 10.4153/CMB-2004-031-8
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     title = {Classifying {Spaces} for {Monoidal} {Categories} {Through} {Geometric} {Nerves}},
     journal = {Canadian mathematical bulletin},
     pages = {321--331},
     year = {2004},
     volume = {47},
     number = {3},
     doi = {10.4153/CMB-2004-031-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-031-8/}
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