A note on the Huq-commutativity of normal monomorphisms
Category Theory
2022-06-28 v1
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.
Cite
@article{arxiv.2206.12855,
title = {A note on the Huq-commutativity of normal monomorphisms},
author = {James Richard Andrew Gray and Tamar Janelidze-Gray},
journal= {arXiv preprint arXiv:2206.12855},
year = {2022}
}