## Homology, Homotopy and Applications

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

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

A. R. Garzón and R. Pérez

#### 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

**Permanent link to this document**

https://projecteuclid.org/euclid.hha/1355321063

**Mathematical Reviews number (MathSciNet)**

MR2954665

**Zentralblatt MATH identifier**

1242.18011

**Subjects**

Primary: 18D05: Double categories, 2-categories, bicategories and generalizations 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23] 55P15: Classification of homotopy type 55P48: Loop space machines, operads [See also 18D50]

**Keywords**

Homotopy colimit simplicial set bicategory braided monoidal category

#### Citation

Garzón, A. R.; Pérez, R. A homotopy colimit theorem for diagrams of braided monoidal categorie. Homology Homotopy Appl. 14 (2012), no. 1, 19--32. https://projecteuclid.org/euclid.hha/1355321063