Homological kernels of monoidal functors
Category Theory
2022-10-18 v3
Abstract
We show that each rigid monoidal category A over a field defines a family of universal tensor categories, which together classify all faithful monoidal functors from A to tensor categories. Each of the universal tensor categories classifies monoidal functors of a given 'homological kernel' and can be realised as a sheaf category, not necessarily on A. This yields a theory of 'local abelian envelope' which completes the notion of monoidal abelian envelopes.
Cite
@article{arxiv.2107.02374,
title = {Homological kernels of monoidal functors},
author = {Kevin Coulembier},
journal= {arXiv preprint arXiv:2107.02374},
year = {2022}
}