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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.AT2025
Poincaré-Birkhoff-Witt Theorems in Higher Algebra
Omar Antolín-Camarena, Lukas Brantner, Gijs Heuts
We extend the classical Poincaré-Birkhoff-Witt theorem to higher algebra by establishing a version that applies to spectral Lie algebras. We deduce this statement from a basic rela…