The balanced tensor product of module categories
Quantum Algebra
2019-07-17 v3 Category Theory
Abstract
The balanced tensor product M (x)_A N of two modules over an algebra A is the vector space corepresenting A-balanced bilinear maps out of the product M x N. The balanced tensor product M [x]_C N 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 x 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.
Cite
@article{arxiv.1406.4204,
title = {The balanced tensor product of module categories},
author = {Christopher L. Douglas and Christopher Schommer-Pries and Noah Snyder},
journal= {arXiv preprint arXiv:1406.4204},
year = {2019}
}
Comments
19 pages; v3 is author-final version