A Quillen model for classical Morita theory and a tensor categorification of the Brauer group
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Tabuada_A Quillen.pdf
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Author(s)
Dell'Ambrogio, Ivo
Trigo Neri Tabuada, Goncalo Jorge
Date Issued
April 2014
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/j.jpaa.2014.04.004
