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Two- and one-dimensional combinatorial exactness structures in Kurosh-Amitsur radical theory. I. (English. French summary) Zbl 1397.18008

The authors propose a new version of combinatorial exactness structure for the abstract theory of Kurosh-Amitsur radicals introduced in [G. Janelidze and L. Márki, Commun. Algebra 31, No. 1, 241–258 (2003; Zbl 1025.17003)].

MSC:

18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
18A32 Factorization systems, substructures, quotient structures, congruences, amalgams
18A99 General theory of categories and functors
18G50 Nonabelian homological algebra (category-theoretic aspects)
18G55 Nonabelian homotopical algebra (MSC2010)
16N80 General radicals and associative rings
06A15 Galois correspondences, closure operators (in relation to ordered sets)

Citations:

Zbl 1025.17003
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