%0 Journal Article %T From torsion theories to closure operators and factorization systems %J Categories and General Algebraic Structures with Applications %I Shahid Beheshti University %Z 2345-5853 %A Grandis, Marco %A Janelidze, George %D 2020 %\ 01/01/2020 %V 12 %N 1 %P 89-121 %! From torsion theories to closure operators and factorization systems %K Exact sequence %K torsion theory %K closure operator %K factorization system %K ideal of null morphisms %R 10.29252/cgasa.12.1.89 %X 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]. %U https://cgasa.sbu.ac.ir/article_87116_929764e335e7d4c92a5611139b9e065a.pdf