Comonadic approach to pretorsion theories
Category Theory
2026-01-19 v1
Abstract
We present a comonadic approach to pretorsion theories on semiexact categories, i.e. categories equipped with a closed ideal of null morphisms that admits all kernels and all cokernels. We first prove that bihereditary pretorsion theories are comonadic in a 2-dimensional sense over the 2-category of semiexact categories with naturally chosen 1-cells. We then extend the built pseudo-comonad to guarantee that all pretorsion theories are pseudo-coalgebras. But interestingly, not all pseudo-coalgebras are pretorsion theories. Rather, pseudo-coalgebras give a generalized notion of pretorsion theory.
Cite
@article{arxiv.2601.11472,
title = {Comonadic approach to pretorsion theories},
author = {Elena Caviglia and Zurab Janelidze and Luca Mesiti},
journal= {arXiv preprint arXiv:2601.11472},
year = {2026}
}