Classifying Spaces for Monoidal Categories Through Geometric Nerves

Canadian mathematical bulletin

关键词: monoidal category;    pseudo-simplicial category;    simplicial set;    classifying space;    homotopy type;   

DOI  :  10.4153/CMB-2004-031-8

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

The usual constructions of classifying spaces for monoidal categoriesproduce CW-complexes withmany cells that, moreover, do not have any proper geometric meaning.However, geometric nerves ofmonoidal categories are very handy simplicial sets whose simpliceshavea pleasing geometricdescription: they are diagrams with the shape of the 2-skeleton oforiented standard simplices. Thepurpose of this paper is to prove that geometric realizations ofgeometric nerves are classifyingspaces for monoidal categories.

【 授权许可】

Unknown