From torsion theories to closure operators and factorization systems

Document Type : Research Paper


1 Dipartimento di Matematica, Universit\`a di Genova, Via Dodecaneso 35, 16146-Genova, Italy

2 Department of Mathematics and Applied Mathematics, University of Cape Town, South Africa.



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].


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