Homology, Homotopy and Applications

Volume 14 (2012)

Number 1

A homotopy colimit theorem for diagrams of braided monoidal categories

Pages: 19 – 32

DOI: http://dx.doi.org/10.4310/HHA.2012.v14.n1.a2

Authors

A.R. Garzón (Departamento de Álgebra, Facultad de Ciencias, Universidad de Granada, Spain)

R. Pérez (Departamento de Álgebra, Facultad de Ciencias, Universidad de Granada, Spain)

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 $\mathcal{B}$ 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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