AI 中文总结
本文提出一种在给定范畴上建立诺特形式存在性的转移策略，并证明广泛类别的本质代数与拓扑范畴（如小范畴、拓扑空间等）均具有诺特形式。
AI 中文摘要
范畴上的诺特形式使得人们能够在该范畴中表述并证明同态定理，例如同构定理和同调代数的图表引理。本文我们发展了一种在给定范畴上建立诺特形式存在性的策略，该策略使得人们能够为广泛的具象范畴找到诺特形式。虽然已知所有半阿贝尔范畴、Grandis正合范畴和代数范畴都具有诺特形式，我们现在还确立了本质代数范畴和拓扑范畴的广泛类别也具有诺特形式，这些类别包括小范畴、群胚、拓扑空间、扩展伪度量空间、逼近空间、图、可测空间和无公理关系结构的范畴。
英文摘要
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.
Comments63 pages
