Lax Distributivity and a Characterization of Abelian Categories
Category Theory
2026-07-28 v1
Abstract
We show that abelian categories can be characterized as structures consisting of a colax algebra and a lax algebra connected by a lax mixed rewriting rule. To this end we develop a theory of lax rewriting rules for pairs of lax-lax and colax-lax algebras over 2-monads.
Cite
@article{arxiv.2607.25740,
title = {Lax Distributivity and a Characterization of Abelian Categories},
author = {Martin Markl and Dominik Trnka},
journal= {arXiv preprint arXiv:2607.25740},
year = {2026}
}
Comments
32 pages