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.
HOMOLOGICAL LEMMAS IN A NON-POINTED CONTEXT / A. Cappelletti, A. Montoli. - In: THEORY AND APPLICATIONS OF CATEGORIES. - ISSN 1201-561X. - 44:(2025), pp. 544-564.
HOMOLOGICAL LEMMAS IN A NON-POINTED CONTEXT
A. MontoliUltimo
2025
Abstract
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.
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