Homological Lemmas in a Non-pointed Context

2024/05/17 by Andrea Cappelletti, Cappelletti, Andrea, Andrea Montoli +1 · 1 citation
Computer Science · Mathematics · #03C05 #18A20 #18E08 #18E13 #18G50 #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2405.11038

openalex publication_date 2024/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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