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arXiv · 2308.16843

Homotopy torsion theories

Sandra Mantovani·Mariano Messora·Enrico M. Vitale
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Abstract

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 pre-pointed 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.

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Sandra Mantovani, Mariano Messora, Enrico M. Vitale. 2023-08-31. Homotopy torsion theories. https://arxiv.org/abs/2308.16843

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