Comonadic approach to pretorsion theories
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909992616984576 |
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| author | Caviglia, Elena Janelidze, Zurab Mesiti, Luca |
| author_facet | Caviglia, Elena Janelidze, Zurab Mesiti, Luca |
| contents | We present a comonadic approach to pretorsion theories on semiexact categories, i.e. categories equipped with a closed ideal of null morphisms that admits all kernels and all cokernels. We first prove that bihereditary pretorsion theories are comonadic in a 2-dimensional sense over the 2-category of semiexact categories with naturally chosen 1-cells. We then extend the built pseudo-comonad to guarantee that all pretorsion theories are pseudo-coalgebras. But interestingly, not all pseudo-coalgebras are pretorsion theories. Rather, pseudo-coalgebras give a generalized notion of pretorsion theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11472 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Comonadic approach to pretorsion theories Caviglia, Elena Janelidze, Zurab Mesiti, Luca Category Theory 18E40, 18C15, 18N10 We present a comonadic approach to pretorsion theories on semiexact categories, i.e. categories equipped with a closed ideal of null morphisms that admits all kernels and all cokernels. We first prove that bihereditary pretorsion theories are comonadic in a 2-dimensional sense over the 2-category of semiexact categories with naturally chosen 1-cells. We then extend the built pseudo-comonad to guarantee that all pretorsion theories are pseudo-coalgebras. But interestingly, not all pseudo-coalgebras are pretorsion theories. Rather, pseudo-coalgebras give a generalized notion of pretorsion theory. |
| title | Comonadic approach to pretorsion theories |
| topic | Category Theory 18E40, 18C15, 18N10 |
| url | https://arxiv.org/abs/2601.11472 |