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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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Journal of Pure and Applied Algebra
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.