Classifying Spaces for Monoidal Categories Through Geometric Nerves

• Autores: Manuel Bullejos Lorenzo, Antonio M. Cegarra
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 47, Nº 3, 2004, págs. 321-331
• Idioma: inglés
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• Resumen

  • 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.