We give a new criterion for when two Bourn-normal monomorphisms with the same codomain in a unital category Huq-commute. We use this to prove that in a unital category, satisfying the (additional) condition that a morphism is a monomorphism if and only if its kernel is a zero morphism, two 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.
Keywords: unital category, Huq-commutes, subtractive category, normal category
2020 MSC: 18E13, 18E08, 18E99
Theory and Applications of Categories, Vol. 45, 2026, No. 41, pp 1732-1747.
Published 2026-07-02.
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