Transfer theory for noetherian forms
Abstract
A noetherian form over a category enables one to formulate and prove homomorphism theorems in that category, such as the isomorphism theorems and the diagram lemmas of homological algebra. In this paper we develop a strategy for establishing existence of a noetherian form over a given category, which enables one to find noetherian forms for a broad range of concrete categories. While it was already known that all semi-abelian categories, Grandis exact categories and algebraic categories have noetherian forms, we now establish that so do wide classes of essentially algebraic and topological categories, which include the categories of small categories, groupoids, topological spaces, extended pseudometric spaces, approach spaces, graphs, measurable spaces and axiom-free relational structures.
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BibTeX
@misc{dayaram2026transfer,
title = {{Transfer theory for noetherian forms}},
author = {Kishan Dayaram and Zurab Janelidze and Francois van Niekerk},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33469},
eprint = {2609.33469},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33469},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Transfer theory for noetherian forms
AU - Kishan Dayaram
AU - Zurab Janelidze
AU - Francois van Niekerk
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33469
UR - https://arxiv.org/abs/2609.33469
AB - A noetherian form over a category enables one to formulate and prove homomorphism theorems in that category, such as the isomorphism theorems and the diagram lemmas of homological algebra. In this paper we develop a strategy for establishing existence of a noetherian form over a given category, which enables one to find noetherian forms for a broad range of concrete categories. While it was already known that all semi-abelian categories, Grandis exact categories and algebraic categories have noetherian forms, we now establish that so do wide classes of essentially algebraic and topological categories, which include the categories of small categories, groupoids, topological spaces, extended pseudometric spaces, approach spaces, graphs, measurable spaces and axiom-free relational structures.
ER -