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arXiv · 2608.23804

Torsion and exactness

Marino Gran·George Janelidze
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Abstract

We give an equivalent definition of a non-pointed torsion theory, also called a pretorsion theory in the literature. This uses a new, more general, notion of a near-torsion theory, and does not use non-pointed exactness. Furthermore, a general method of associating the `largest' (non-pointed) torsion theory to any given near-torsion theory is described. We also describe a near-torsion theory formed by the class of cokernel diagrams and the class of kernel diagrams in a pointed category with kernels and cokernels, and its associated torsion theory.

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Marino Gran, George Janelidze. 2026-08-24. Torsion and exactness. https://arxiv.org/abs/2608.23804

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