2011/11/23 by Tomas Everaert, Marino Gran · 2 citations
Computer Science · Mathematics · #Abelian category #Abelian group #Algebra over a field #Algebraic structures and combinatorial models #Functor #Functor category #Homological algebra #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Mathematics #Natural transformation #Pure mathematics #Topological and Geometric Data Analysis #Torsion (gastropod) #math.CT #msc:08B05 #msc:18A40 #msc:18E40 #msc:18G10 #msc:18G50 #msc:20J05
paper · pdf · doi:10.1016/j.jpaa.2014.12.015
published as Journal of Pure and Applied Algebra, Volume 219, Issue 8, August 2015, Pages 3629-3676
arxiv created 2011/11/23 · openalex publication_date 2014/12/12 · arxiv updated 2015/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Protoadditive functors are designed to replace additive functors in a non-abelian setting. Their properties are studied, in particular in relationship with torsion theories, Galois theory, homology and factorisation systems. It is shown how a protoadditive torsion-free reflector induces a chain of derived torsion theories in the categories of higher extensions, similar to the Galois structures of higher central extensions previously considered in semi-abelian homological algebra. Such higher central extensions are also studied, with respect to Birkhoff subcategories whose reflector is protoadditive or, more generally, factors through a protoadditive reflector. In this way we obtain simple descriptions of the non-abelian derived functors of the reflectors via higher Hopf formulae. Various examples are considered in the categories of groups, compact groups, internal groupoids in a semi-abelian category, and other ones.