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Model structures on the
category of small double categories
Thomas M Fiore, Simona Paoli and Dorette Pronk |
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Algebraic & Geometric Topology 8 (2008) 1855–1959
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Abstract |
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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. |
Keywords
categorification, colimit, double category, fundamental
category, fundamental double category, horizontal
categorification, internal category, model structure,
transfer of model structure, $2$–category, $2$–monad
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Mathematical Subject Classification 2000
Primary: 18D05, 18G55
Secondary: 55P99, 55U10
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References |
Publication
Received: 26 October 2007
Revised: 27 August 2008
Accepted: 27 August 2008
Published: 21 October 2008
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Authors |
| Thomas M Fiore | |
| Department of Mathematics University of Chicago 5734 South University Chicago, IL 60637 USA and Departament de Matemàtiques Universitat Autònoma de Barcelona 08193 Bellaterra (Barcelona) Spain |
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| http://www.math.uchicago.edu/~fiore/ | |
| Simona Paoli | |
| Department of Mathematics Macquarie University NSW 2109 Australia |
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| http://www.ics.mq.edu.au/~simonap/ | |
| Dorette Pronk | |
| Chase Building Department of Mathematics and Statistics Dalhousie University Halifax, Nova Scotia Canada B3H 3J5 Canada |
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| http://www.mathstat.dal.ca/Faculty/pronk.htm | |
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