Morita Bicategories of Algebras and Duality Involutions
Abstract
The notion of a weak duality involution on a bicategory was recently introduced by Shulman in [arXiv:1606.05058]. We construct a weak duality involution on the fully dualisable part of $\text{Alg}$, the Morita bicategory of finitedimensional kalgebras. The 2category $\text{KV}$ of KapranovVoevodsky kvector spaces may be equipped with a canonical strict duality involution. We show that the pseudofunctor $\text{Rep}: \text{Alg}^{fd} \to \text{KV}$ sending an algebra to its category of finitedimensional modules may be canonically equipped with the structure of a duality pseudofunctor. Thus $\text{Rep}$ is a strictification in the sense of Shulman's strictification theorem for bicategories with a weak duality involution. Finally, we present a general setting for duality involutions on the Morita bicategory of algebras in a semisimple symmetric finite tensor category.
 Publication:

arXiv eprints
 Pub Date:
 February 2019
 arXiv:
 arXiv:1902.04866
 Bibcode:
 2019arXiv190204866L
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Quantum Algebra;
 18D05;
 16D90
 EPrint:
 26 pages