A note on the Huq-commutativity of normal monomorphisms
James Richard Andrew Gray, Tamar Janelidze-Gray

TL;DR
This paper provides an alternative criterion for Huq-commutativity of Bourn-normal monomorphisms in unital categories, extending known results from protomodular contexts to more general settings.
Contribution
It introduces a new criterion for Huq-commutativity and generalizes several known facts from protomodular categories to broader unital categories.
Findings
Huq-commutativity characterized by trivial pullback in certain categories
Normal monomorphisms with same codomain Huq-commute under specific conditions
Extension of protomodular results to more general unital categories
Abstract
We give an alternative criteria for when a pair of Bourn-normal monomorphisms Huq-commute in a unital category. We use this to prove that in a unital category, in which a morphism is a monomorphism if and only if its kernel is zero morphism, a pair of Bourn-normal monomorphisms with the same codomain Huq-commute as soon as they have trivial pullback. As corollaries we show that several facts known only in the protomodular context are in fact true in more general contexts.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Algebraic structures and combinatorial models
