Toposes have an optimal noetherian form
Category Theory
2025-01-29 v3 Group Theory
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.
Cite
@article{arxiv.2304.03814,
title = {Toposes have an optimal noetherian form},
author = {Zurab Janelidze and Francois van Niekerk},
journal= {arXiv preprint arXiv:2304.03814},
year = {2025}
}
Comments
69 pages, submitted for publication