GrothendieckVerdier duality in categories of bimodules and weak module functors
Abstract
Various monoidal categories, including suitable representation categories of vertex operator algebras, admit natural GrothendieckVerdier duality structures. We recall that such a GrothendieckVerdier category comes with two tensor products which should be related by distributors obeying pentagon identities. We discuss in which circumstances these distributors are isomorphisms. This is achieved by taking the perspective of module categories over monoidal categories, using in particular the natural weak module functor structure of internal Homs and internal coHoms. As an illustration, we exhibit these concepts concretely in the case of categories of bimodules over associative algebras.
 Publication:

arXiv eprints
 Pub Date:
 June 2023
 DOI:
 10.48550/arXiv.2306.17668
 arXiv:
 arXiv:2306.17668
 Bibcode:
 2023arXiv230617668F
 Keywords:

 Mathematics  Category Theory;
 High Energy Physics  Theory;
 Mathematics  Quantum Algebra;
 18M10;
 16B50;
 81R10
 EPrint:
 24 pages