Tobias Barthel

collaborators

4 papers

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 $Set$ of sets. This result is deduced fro…

math.AG2025

Higher Zariski Geometry

Ko Aoki, Tobias Barthel, Anish Chedalavada +2

We revisit the classical constructions of tensor-triangular geometry in the setting of stably symmetric monoidal idempotent-complete $\infty$ -categories, henceforth referred to as…

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…

math.AT2017

On the comparison of stable and unstable $p$ -completion

Tobias Barthel, A. K. Bousfield

In this note we show that a $p$ -complete nilpotent space $X$ has a $p$ -complete suspension spectrum if and only if its homotopy groups $π_{*} X$ are bounded $p$ -torsion. In contrast,…

The nine model category structures on the category of sets

Higher Zariski Geometry

Cohen's theorem in tensor triangular geometry

On the comparison of stable and unstable p-completion

On the comparison of stable and unstable $p$ -completion