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...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Elsevier
2016
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| Online Access: | http://hdl.handle.net/1721.1/105483 https://orcid.org/0000-0001-5558-9236 |
| Summary: | 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. |
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