8 citations · 45 across the 26 of their papers we have counts for
26 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…
Polarities, voltages, and capacitors: a categorical approach to hulls, envelopes, and completions
Ivan Di Liberti, Martino Lupini
This article provides a general framework in the context of category theory where one can recognize as particular instances of the same abstract construction several notions of com…
Craig Interpolation for Subgeometric Logics
Ivan Di Liberti, Lingyuan Ye
We show that a vast class of finitary fragments of geometric logic admit a form of Craig interpolation property. In doing so, we provide a new dictionary to import technology from…
Classifying Infinity Topoi via Weighted Limits
Ivan Di Liberti, Nicholas Meadows
We construct classifying -topoi by showing that the -category of topoi has weighted limits. We show that several prestacks of interest have a classifying topos,…
Logic and Concepts in the 2-category of Topoi
Ivan Di Liberti, Lingyuan Ye
We use Kan injectivity to axiomatise concepts in the 2-category of topoi. We showcase the expressivity of this language through many examples, and we establish some aspects of the…
Sketches and Classifying Logoi
Ivan Di Liberti, Gabriele Lobbia
Inspired by the theory of classifying topoi for geometric theories, we define rounded sketches and logoi and provide the notion of classifying logos for a rounded sketch. Rounded s…
Topoi with enough points
Ivan Di Liberti, Morgan Rogers
We extend Deligne's original argument showing that locally coherent topoi have enough points, clarified using collage diagrams. We show that our refinement of Deligne's technique c…
Adjoint functor theorems for lax-idempotent pseudomonads
Nathanael Arkor, Ivan Di Liberti, Fosco Loregian
For each pair of lax-idempotent pseudomonads and , for which is locally fully faithful and distributes over , we establish an adjoint functor theorem, relating $R…
Duality for coalgebras for Vietoris and monadicity
Marco Abbadini, Ivan Di Liberti
We prove that the opposite of the category of coalgebras for the Vietoris endofunctor on the category of compact Hausdorff spaces is monadic over Set. We deliver an analogous resul…
The geometry of Coherent topoi and Ultrastructures
Ivan Di Liberti
We show that coherent topoi are right Kan injective with respect to flat embeddings of topoi. We recover the ultrastructure on their category of points as a consequence of this res…
KZ-pseudomonads and Kan Injectivity
Ivan Di Liberti, Gabriele Lobbia, Lurdes Sousa
We introduce the notion of Kan injectivity in 2-categories and study its properties. For an adequate 2-category , we show that every set of morphisms ind…
Bi-accessible and bipresentable 2-categories
Ivan Di Liberti, Axel Osmond
We develop a 2-dimensional version of accessibility and presentability compatible with the formalism of flat pseudofunctors. First we give prerequisites on the different notions of…
Context, Judgement, Deduction
Greta Coraglia, Ivan Di Liberti
We introduce judgemental theories and their calculi as a general framework to present and study deductive systems. As an exemplification of their expressivity, we approach dependen…
Exponentiable Grothendieck categories in flat Algebraic Geometry
Ivan Di Liberti, Julia Ramos González
We introduce and describe the -category of Grothendieck categories and flat morphisms between them. First, we show that the tensor product of locally pres…
Functorial Semantics for Partial Theories
Ivan Di Liberti, Fosco Loregian, Chad Nester +1
We provide a Lawvere-style definition for partial theories, extending the classical notion of equational theory by allowing partially defined operations. As in the classical case,…
Formal Model Theory & Higher Topology
Ivan Di Liberti
We study the -categories BIon, of (generalized) bounded ionads, and , of accessible categories with directed colimits, as an abstract framework to approach formal…
The Scott adjunction
Ivan Di Liberti
We introduce and study the Scott adjunction, relating accessible categories with directed colimits to topoi. Our focus is twofold, we study both its applications to formal model th…
Towards Higher Topology
Ivan Di Liberti
We categorify the adjunction between locales and topological spaces, this amounts to an adjunction between (generalized) bounded ionads and topoi. We show that the adjunction is id…
General facts on the Scott Adjunction
Ivan Di Liberti
We introduce, comment and develop the Scott adjunction, mostly from the point of view of a category theorist. Besides its technical and conceptual aspects, in a nutshell we provide…
Enriched Locally Generated Categories
Ivan Di Liberti, Jiří Rosický
We introduce the notion of -locally generated category for a factorization system and study its properties. We offer a Gabriel-Ulmer dualit…
Codensity: Isbell duality, pro-objects, compactness and accessibility
Ivan Di Liberti
We study codensity monads induced by (mostly small, mostly dense) full subcategories . These monads behave quite similarly, we show some connections with the Isbel…
Gabriel-Ulmer duality for topoi and its relation with site presentations
Ivan Di Liberti, Julia Ramos González
Let be a regular cardinal. We study Gabriel-Ulmer duality when one restricts the 2-category of locally -presentable categories with -accessible right adjoints to its loca…
On the unicity of formal category theories
Ivan Di Liberti, Fosco Loregian
We prove an equivalence between cocomplete Yoneda structures and certain proarrow equipments on a 2-category . In order to do this, we recognize the presheaf constructi…
Accessibility and presentability in 2-categories
Ivan Di Liberti, Fosco Loregian
We outline a definition of accessible and presentable objects in a 2-category endowed with a "KZ context", that is to say a pair of lax-idempotent monads interacting i…