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Torsion theories and radicals in normal categories
Clementino, M. M.; Dikranjan, D.; Tholen, W.We introduce a relativized notion of (semi)normalcy for categories that come equipped with a proper stable factorization system, and we use radicals (in the sense of module theory) and normal closure operators in order to study torsion theories in such categories. Our results generalize and complement recent studies in the realm of semi-abelian and, in part, homological categories. In particular, we characteriz...
Prolocalisations of homological categories
Borceux, F.; Clementino, M. M.; Gran, M.; Sousa, L.A prolocalisation of an homological (resp. semi-abelian) category is a regular full re ective subcategory, whose re ection preserves short exact sequences. We study the closure operator and the torsion theory associated with such a situation. We pay special attention to the bered, the epire ective and the monore ective cases. We give examples in algebra, topos theory, functional analysis. ; Université Catho...
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