Coherent and ideal actions in ideally exact categories
Category Theory
2026-05-25 v3 Logic
Rings and Algebras
Abstract
In the context of ideally exact categories, we introduce the notions of internal coherent action and internal ideal action that generalise different aspects of unital actions of rings and algebras. We prove that every ideal action is coherent, and that the converse statement holds in some relevant ideally exact contexts. Furthermore, a connection with G. Janelidze's notion of semidirect product in ideally exact categories is analysed.
Cite
@article{arxiv.2507.06124,
title = {Coherent and ideal actions in ideally exact categories},
author = {Manuel Mancini and Giuseppe Metere and Federica Piazza},
journal= {arXiv preprint arXiv:2507.06124},
year = {2026}
}
Comments
Final version, accepted for publication