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arXiv · 2304.03814

Toposes have an optimal noetherian form

Zurab Janelidze·Francois van Niekerk
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Abstract

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.

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Zurab Janelidze, Francois van Niekerk. 2023-04-07. Toposes have an optimal noetherian form. https://arxiv.org/abs/2304.03814

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