English

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.

Keywords

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

R2 v1 2026-06-22T04:39:49.725Z