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math.CT2025
The nine model category structures on the category of sets
Omar Antolín-Camarena, Tobias Barthel
We give a proof of the folklore theorem, attributed to Goodwillie, that there are precisely nine model structures on the category of sets. This result is deduced fro…
math.CT2025
Cohen's theorem in tensor triangular geometry
Tobias Barthel
A theorem of Cohen from 1950 states that a commutative ring is Noetherian if and only if every prime ideal is finitely generated. In this note, we establish analogues of this resul…