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2008 Model structures on the category of small double categories
Thomas M Fiore, Simona Paoli, Dorette Pronk
Algebr. Geom. Topol. 8(4): 1855-1959 (2008). DOI: 10.2140/agt.2008.8.1855


In this paper we obtain several model structures on DblCat, 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 Cat and take as our weak equivalences various internal equivalences defined via Grothendieck topologies. Thirdly, DblCat inherits a model structure as a category of algebras over a 2–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.


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Thomas M Fiore. Simona Paoli. Dorette Pronk. "Model structures on the category of small double categories." Algebr. Geom. Topol. 8 (4) 1855 - 1959, 2008.


Received: 26 October 2007; Revised: 27 August 2008; Accepted: 27 August 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1159.18302
MathSciNet: MR2449004
Digital Object Identifier: 10.2140/agt.2008.8.1855

Primary: 18D05, 18G55
Secondary: 55P99, 55U10

Rights: Copyright © 2008 Mathematical Sciences Publishers


Vol.8 • No. 4 • 2008
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