A homotopy colimit theorem for diagrams of braided monoidal categories

Thomason’s Homotopy Colimit Theorem has been extended to bicategories and this extension can be adapted, through the delooping principle, to a corresponding theorem for diagrams of monoidal categories. In this version, we show that the homotopy type of the diagram can also be represented by a genuine simplicial set nerve associated with it. This suggests the study of a homotopy colimit theorem, for diagrams $\mathcal{B}$ of braided monoidal categories, by means of a simplicial set nerve of the diagram. We prove that it is weak homotopy equivalent to the homotopy colimit of the diagram, of simplicial sets, obtained from composing $\mathcal{B}$ with the geometric nerve functor of braided monoidal categories.

Keywords

homotopy colimit, simplicial set, bicategory, braided monoidal category

2010 Mathematics Subject Classification

18D05, 18D10, 55P15, 55P48

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Published 13 July 2012