EilenbergWatts calculus for finite categories and a bimodule Radford $S^4$ theorem
Abstract
We obtain Morita invariant versions of EilenbergWatts type theorems, relating Deligne products of finite linear categories to categories of left exact as well as of right exact functors. This makes it possible to switch between different functor categories as well as Deligne products, which is often very convenient. For instance, we can show that applying the equivalence from left exact to right exact functors to the identity functor, regarded as a left exact functor, gives a Nakayama functor. The equivalences of categories we exhibit are compatible with the structure of module categories over finite tensor categories. This leads to a generalization of Radford's $S^4$theorem to bimodule categories. We also explain the relation of our construction to relative Serre functors on module categories that are constructed via inner Hom functors.
 Publication:

arXiv eprints
 Pub Date:
 December 2016
 arXiv:
 arXiv:1612.04561
 Bibcode:
 2016arXiv161204561F
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Category Theory;
 Mathematics  Quantum Algebra;
 Mathematics  Rings and Algebras;
 16T05;
 18D10;
 16Gxx
 EPrint:
 41 pages. Typos corrected, literature updated, several minor additions