TY - JOUR ID - 87116 TI - From torsion theories to closure operators and factorization systems JO - Categories and General Algebraic Structures with Applications JA - CGASA LA - en SN - 2345-5853 AU - Grandis, Marco AU - Janelidze, George AD - Dipartimento di Matematica, Universit\`a di Genova, Via Dodecaneso 35, 16146-Genova, Italy AD - Department of Mathematics and Applied Mathematics, University of Cape Town, South Africa. Y1 - 2020 PY - 2020 VL - 12 IS - 1 SP - 89 EP - 121 KW - Exact sequence KW - torsion theory KW - closure operator KW - factorization system KW - ideal of null morphisms DO - 10.29252/cgasa.12.1.89 N2 - Torsion theories are here extended to categories equipped with an ideal of 'null morphisms', or equivalently a full subcategory of 'null objects'. Instances of this extension include closure operators viewed as generalised torsion theories in a 'category of pairs', and factorization systems viewed as torsion theories in a category of morphisms. The first point has essentially been treated in [15]. UR - https://cgasa.sbu.ac.ir/article_87116.html L1 - https://cgasa.sbu.ac.ir/article_87116_929764e335e7d4c92a5611139b9e065a.pdf ER -