Toposes have an optimal noetherian form
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916585889857536 |
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| author | Janelidze, Zurab van Niekerk, Francois |
| author_facet | Janelidze, Zurab van Niekerk, Francois |
| contents | A noetherian form is an abstract self-dual framework suitable for establishing homomorphism theorems (such as the isomorphism theorems and homological diagram lemmas) for group-like structures. In this paper we identify and carry out an axiomatic analysis of a particular class of noetherian forms which exist for both group-like structures and for sheaves. More abstractly, such noetherian forms can be produced from all semi-abelian categories, Grandis exact categories and toposes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2304_03814 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Toposes have an optimal noetherian form Janelidze, Zurab van Niekerk, Francois Category Theory Group Theory 18D30, 18A32, 06B75, 08A30, 06A15, 18E13, 18B25, 18G50, 08C05 A noetherian form is an abstract self-dual framework suitable for establishing homomorphism theorems (such as the isomorphism theorems and homological diagram lemmas) for group-like structures. In this paper we identify and carry out an axiomatic analysis of a particular class of noetherian forms which exist for both group-like structures and for sheaves. More abstractly, such noetherian forms can be produced from all semi-abelian categories, Grandis exact categories and toposes. |
| title | Toposes have an optimal noetherian form |
| topic | Category Theory Group Theory 18D30, 18A32, 06B75, 08A30, 06A15, 18E13, 18B25, 18G50, 08C05 |
| url | https://arxiv.org/abs/2304.03814 |