A Quillen model for classical Morita theory and a tensor categorification of the Brauer group
Let KK be a commutative ring. In this article we construct a well-behaved symmetric monoidal Quillen model structure on the category of small KK-categories which enhances classical Morita theory. Making use of it, we then obtain the usual categorification of the Brauer group and of its functoriality...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Elsevier
2016
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| Online Access: | http://hdl.handle.net/1721.1/105483 https://orcid.org/0000-0001-5558-9236 |
| _version_ | 1826210433272381440 |
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| author | Dell'Ambrogio, Ivo Trigo Neri Tabuada, Goncalo Jorge |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Dell'Ambrogio, Ivo Trigo Neri Tabuada, Goncalo Jorge |
| author_sort | Dell'Ambrogio, Ivo |
| collection | MIT |
| description | Let KK be a commutative ring. In this article we construct a well-behaved symmetric monoidal Quillen model structure on the category of small KK-categories which enhances classical Morita theory. Making use of it, we then obtain the usual categorification of the Brauer group and of its functoriality. Finally, we prove that the (contravariant) corestriction map for finite Galois extensions also lifts to this categorification. |
| first_indexed | 2024-09-23T14:49:49Z |
| format | Article |
| id | mit-1721.1/105483 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:49:49Z |
| publishDate | 2016 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/1054832022-10-01T22:46:00Z A Quillen model for classical Morita theory and a tensor categorification of the Brauer group Dell'Ambrogio, Ivo Trigo Neri Tabuada, Goncalo Jorge Massachusetts Institute of Technology. Department of Mathematics Trigo Neri Tabuada, Goncalo Jorge Let KK be a commutative ring. In this article we construct a well-behaved symmetric monoidal Quillen model structure on the category of small KK-categories which enhances classical Morita theory. Making use of it, we then obtain the usual categorification of the Brauer group and of its functoriality. Finally, we prove that the (contravariant) corestriction map for finite Galois extensions also lifts to this categorification. Fundação para a Ciência e a Tecnologia (Portugal) (PEst-OE/MAT/UI0297/2011) NEC Corporation (NEC Award 2742738) 2016-11-30T20:33:38Z 2016-11-30T20:33:38Z 2014-04 2014-03 Article http://purl.org/eprint/type/JournalArticle 00224049 http://hdl.handle.net/1721.1/105483 Dell’Ambrogio, Ivo, and Gonçalo Tabuada. “A Quillen Model for Classical Morita Theory and a Tensor Categorification of the Brauer Group.” Journal of Pure and Applied Algebra 218, no. 12 (December 2014): 2337–2355. https://orcid.org/0000-0001-5558-9236 en_US http://dx.doi.org/10.1016/j.jpaa.2014.04.004 Journal of Pure and Applied Algebra Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier arXiv |
| spellingShingle | Dell'Ambrogio, Ivo Trigo Neri Tabuada, Goncalo Jorge A Quillen model for classical Morita theory and a tensor categorification of the Brauer group |
| title | A Quillen model for classical Morita theory and a tensor categorification of the Brauer group |
| title_full | A Quillen model for classical Morita theory and a tensor categorification of the Brauer group |
| title_fullStr | A Quillen model for classical Morita theory and a tensor categorification of the Brauer group |
| title_full_unstemmed | A Quillen model for classical Morita theory and a tensor categorification of the Brauer group |
| title_short | A Quillen model for classical Morita theory and a tensor categorification of the Brauer group |
| title_sort | quillen model for classical morita theory and a tensor categorification of the brauer group |
| url | http://hdl.handle.net/1721.1/105483 https://orcid.org/0000-0001-5558-9236 |
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