## Homology, Homotopy and Applications

### A homotopy colimit theorem for diagrams of braided monoidal categorie

#### Abstract

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 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 B with the geometric nerve functor of braided monoidal categories.

#### Article information

Source
Homology Homotopy Appl., Volume 14, Number 1 (2012), 19-32.

Dates
First available in Project Euclid: 12 December 2012