3 papers
math.CT2024
Local Rigidity and Six Functor Formalisms
Adrian Clough
The coefficient categories of six functor formalisms are often locally rigid, and when this is the case, the exceptional pushforward and pullback adjunctions may be defined formall…
math.AT2024
Global spaces and the homotopy theory of stacks
Adrian Clough, Bastiaan Cnossen, Sil Linskens
We show that the -category of global spaces is equivalent to the homotopy localization of the -category of sheaves on the site of separated differentiable stacks, f…
math.AT2023
The homotopy theory of differentiable sheaves
Adrian Clough
Many important theorems in differential topology relate properties of manifolds to properties of their underlying homotopy types -- defined e.g. using the total singular complex or…