We show that non-pointed versions of the classical homological lemmas hold in regular protomodular categories equipped with a suitable posetal monocoreflective subcategory. Examples of such categories are all protomodular varieties of universal algebras having more than one constant, like the ones of unitary rings, Boolean algebras, Heyting algebras and MV-algebras, their topological models, and the dual category of every elementary topos.
Keywords: homological lemmas, non-pointed regular protomodular categories
2020 MSC: 18G50, 18A20, 18E08, 18E13, 03C05
Theory and Applications of Categories, Vol. 44, 2025, No. 18, pp 544-564.
Published 2025-06-24.
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