Please use this identifier to cite or link to this item:
http://hdl.handle.net/2072/10062
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| Title: | Model structures on the category of small double categories |
| Authors: | Fiore, Thomas M.
Paoli, Simona
Pronk, Dorette A. |
| Other authors: | Centre de Recerca Matemàtica |
| Subjects: | Categories (Matemàtica) |
| Creation Date: | Dec-2007 |
| Publisher: | Centre de Recerca Matemàtica |
| Series/Report no.: | Prepublicacions del Centre de Recerca Matemàtica;778 |
| Abstract: | 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 cofi
brant objects. As part of this program we give explicit descriptions and discuss properties of free double categories, quotient double categories, colimits of double categories, and several nerves and categorifications. |
| CDU: | 512 - Algebra |
| Appears in Collections: | Prepublicacions del Centre de Recerca Matemàtica
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