From torsion theories to closure operators and factorization systems. (English) Zbl 1454.18008

Torsion theories are extended far beyond abelian categories. For this, one needs a subcategory of “null morphisms” and gets two full subcategories, one consists of torsion objects and the other from torsion-free ones. Every morphism from a torsion object to a torsion-free object is null. It leads to a factorization system on the category of morphisms.


18E40 Torsion theories, radicals
18A32 Factorization systems, substructures, quotient structures, congruences, amalgams
06A15 Galois correspondences, closure operators (in relation to ordered sets)
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