The balanced tensor product of module categories

Author: 

Douglas, C
Schommer-Pries, C
Snyder, N

Publication Date: 

3 October 2018

Journal: 

Kyoto Journal of Mathematics

Last Updated: 

2020-06-15T07:08:03.77+01:00

Issue: 

1

Volume: 

59

DOI: 

10.1215/21562261-2018-0006

page: 

167-179

abstract: 

The balanced tensor product M⊗AN of two modules over an algebra A is the vector space corepresenting A-balanced bilinear maps out of the product M×N. The balanced tensor product M⊠CN of two module categories over a monoidal linear category C is the linear category corepresenting C-balanced right-exact bilinear functors out of the product category M×N. We show that the balanced tensor product can be realized as a category of bimodule objects in C, provided the monoidal linear category is finite and rigid.

Symplectic id: 

821734

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article