arXiv Open Access 2020

Internal natural transformations and Frobenius algebras in the Drinfeld center

Jürgen Fuchs Christoph Schweigert

Lihat Sumber

Abstrak

For M and N finite module categories over a finite tensor category C, the category Rex_C(M,N) of right exact module functors is a finite module category over the Drinfeld center Z(C). We study the internal Homs of this module category, which we call internal natural transformations. With the help of certain integration functors that map C-C-bimodule functors to objects of Z(C), we express them as ends over internal Homs and define horizontal and vertical compositions. We show that if M and N are exact C-modules and C is pivotal, then the Z(C)-module Rex_C(M,N) is exact. We compute its relative Serre functor and show that if M and N are even pivotal module categories, then Rex_C(M,N) is pivotal as well. Its internal Ends are then a rich source for Frobenius algebras in Z(C).

Topik & Kata Kunci

math.CT hep-th math.QA

Penulis (2)

Jürgen Fuchs

Christoph Schweigert

Format Sitasi

APA MLA BibTeX

Fuchs, J., Schweigert, C. (2020). Internal natural transformations and Frobenius algebras in the Drinfeld center. https://arxiv.org/abs/2008.04199

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2020
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓