Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 8, Number 4 (2008), 1855-1959.
Model structures on the category of small double categories
In this paper we obtain several model structures on , the category of small double categories. Our model structures have three sources. We first transfer across a categorification-nerve adjunction. Secondly, we view double categories as internal categories in and take as our weak equivalences various internal equivalences defined via Grothendieck topologies. Thirdly, inherits a model structure as a category of algebras over a –monad. Some of these model structures coincide and the different points of view give us further results about cofibrant replacements and cofibrant objects. As part of this program we give explicit descriptions for and discuss properties of free double categories, quotient double categories, colimits of double categories, horizontal nerve and horizontal categorification.
Algebr. Geom. Topol., Volume 8, Number 4 (2008), 1855-1959.
Received: 26 October 2007
Revised: 27 August 2008
Accepted: 27 August 2008
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 18D05: Double categories, 2-categories, bicategories and generalizations 18G55: Homotopical algebra
Secondary: 55P99: None of the above, but in this section 55U10: Simplicial sets and complexes
categorification colimit double category fundamental category fundamental double category horizontal categorification internal category model structure transfer of model structure $2$–category $2$–monad
Fiore, Thomas M; Paoli, Simona; Pronk, Dorette. Model structures on the category of small double categories. Algebr. Geom. Topol. 8 (2008), no. 4, 1855--1959. doi:10.2140/agt.2008.8.1855. https://projecteuclid.org/euclid.agt/1513796920