4 papers
Conceptual completeness for subgeometric logics
Ivan Di Liberti, Umberto Tarantino, Lingyuan Ye
We explore the notion of conceptual completeness for a fragment of geometric logic in the framework developed by the first and third author. Unlike its traditional interpretation a…
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…
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…
A category of arrow algebras for modified realizability
Umberto Tarantino
In this paper we further the study of arrow algebras, simple algebraic structures inducing toposes through the tripos-to-topos construction, by defining appropriate notions of morp…