Nakayama functors for coalgebras and their applications for Frobenius tensor categories
Abstract
We introduce Nakayama functors for coalgebras and investigate their basic properties. These functors are expressed by certain (co)ends as in the finite case discussed by Fuchs, Schaumann, and Schweigert. This observation allows us to define Nakayama functors for Frobenius tensor categories in an intrinsic way. As applications, we establish the categorical Radford $S^4$formula for Frobenius tensor categories and obtain some related results. These are generalizations of works of Etingof, Nikshych, and Ostrik on finite tensor categories and some known facts on coFrobenius Hopf algebras.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.08739
 Bibcode:
 2021arXiv211008739S
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Category Theory;
 Mathematics  Representation Theory;
 18M05;
 16T05
 EPrint:
 48 pages