Homological Lemmas in a Non-pointed Context
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913921606090752 |
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| author | Cappelletti, Andrea Montoli, Andrea |
| author_facet | Cappelletti, Andrea Montoli, Andrea |
| contents | We show that non-pointed versions of the classical homological lemmas hold in regular protomodular categories equipped with a suitable posetal monocoreflective subcategory. Examples of such categories are all protomodular varieties of universal algebras having more than one constant, like the ones of unitary rings, Boolean algebras, Heyting algebras and MV-algebras, their topological models, and the dual category of every elementary topos. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11038 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homological Lemmas in a Non-pointed Context Cappelletti, Andrea Montoli, Andrea Category Theory 18G50, 18A20, 18E08, 18E13, 03C05 We show that non-pointed versions of the classical homological lemmas hold in regular protomodular categories equipped with a suitable posetal monocoreflective subcategory. Examples of such categories are all protomodular varieties of universal algebras having more than one constant, like the ones of unitary rings, Boolean algebras, Heyting algebras and MV-algebras, their topological models, and the dual category of every elementary topos. |
| title | Homological Lemmas in a Non-pointed Context |
| topic | Category Theory 18G50, 18A20, 18E08, 18E13, 03C05 |
| url | https://arxiv.org/abs/2405.11038 |