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A Quillen model for classical Morita theory and a tensor categorification of the Brauer group

Author(s)
Dell'Ambrogio, Ivo; Trigo Neri Tabuada, Goncalo Jorge
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Abstract
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.
Date issued
2014-04
URI
http://hdl.handle.net/1721.1/105483
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Journal of Pure and Applied Algebra
Publisher
Elsevier
Citation
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.
Version: Original manuscript
ISSN
00224049

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