2 papers
math.CT2025
Toposes with enough points as categories of étale spaces
Sam van Gool, Jérémie Marquès, Umberto Tarantino
We extend Makkai duality between coherent toposes and ultracategories to a duality between toposes with enough points and ultraconvergence spaces. Our proof generalizes and simplif…
math.CT2025
Ultracategories via Kan extensions of relative monads
Umberto Tarantino, Joshua Wrigley
Many structured categories of interest are most naturally described as algebras for a relative monad, but turn out nonetheless to be algebras for an ordinary monad. We show that, u…