Homotopy torsion theories

In the context of categories equipped with a structure of nullhomotopies, we introduce the notion of homotopy torsion theory. As special cases, we recover pretorsion theories as well as torsion theories in multi -pointed categories and in prepointed categories. Using the structure of nullhomotopies induced by the canonical string of adjunctions between a category A and the category Arr (A ) of arrows, we give a new proof of the correspondence between orthogonal factorization systems in A and homotopy torsion theories in Arr (A), avoiding the request on the existence of pullbacks and pushouts in A. Moreover, such a correspondence is extended to weakly orthogonal factorization systems and weak homotopy torsion theories. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.