2 citations · 2 across the 7 of their papers we have counts for
8 papers
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…
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 -categories, henceforth referred to as…
Global representation theory: Homological foundations
Miguel Barrero, Tobias Barthel, Luca Pol +2
A global representation is a compatible collection of representations of the outer automorphism groups of the groups belonging to some collection of finite groups . Gl…
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…
The spectrum of excisive functors
Gregory Arone, Tobias Barthel, Drew Heard +1
We prove a thick subcategory theorem for the category of -excisive functors from finite spectra to spectra. This generalizes the Hopkins-Smith thick subcategory theorem (the $d=…
Profinite equivariant spectra and their tensor-triangular geometry
Scott Balchin, David Barnes, Tobias Barthel
We study the tensor-triangular geometry of the category of equivariant -spectra for a profinite group, . Our starting point is the construction of a ``continu…
Prismatic decompositions and rational -spectra
Scott Balchin, Tobias Barthel, J. P. C. Greenlees
We study the tensor-triangular geometry of the category of rational -spectra for a compact Lie group . In particular, we prove that this category can be naturally decomposed…
On the comparison of stable and unstable -completion
Tobias Barthel, A. K. Bousfield
In this note we show that a -complete nilpotent space has a -complete suspension spectrum if and only if its homotopy groups are bounded -torsion. In contrast,…