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

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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Bibliographic Details
Main Authors: Dell'Ambrogio, Ivo (Author), Trigo Neri Tabuada, Goncalo Jorge (Contributor)
Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
Format: Article
Language:English
Published: Elsevier, 2016-11-30T20:33:38Z.
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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.
Fundação para a Ciência e a Tecnologia (Portugal) (PEst-OE/MAT/UI0297/2011)
NEC Corporation (NEC Award 2742738)

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