25 citations · 61 across the 22 of their papers we have counts for
26 papers
On implicit operations and balanced categories
Luca Reggio
The problem of determining whether a category is balanced (i.e., every morphism that is both an epimorphism and a monomorphism is an isomorphism) has been widely investigated, espe…
Beth companions of finitary essentially algebraic theories
Ivan Di Liberti, Luca Reggio
For categories, being balanced (meaning that every arrow that is both epic and monic is an isomorphism) can be regarded as a strong tameness property which plays an important role,…
On the Axioms of Arboreal Categories
Tomáš Jakl, Luca Reggio
Arboreal categories were introduced as an axiomatic framework for game comonads, which provide a comonadic view on many model-comparison games in logic. We demonstrate the inadequa…
Poset-enriched pretoposes and compact ordered spaces
Jérémie Marquès, Luca Reggio
We provide a characterisation of the category of Nachbin's compact ordered spaces as a poset-enriched category. Up to equivalence, is the only non-d…
Existential and positive games: a comonadic and axiomatic view
Samson Abramsky, Thomas Laure, Luca Reggio
A number of model-comparison games central to (finite) model theory, such as pebble and Ehrenfeucht-Fraïssé games, can be captured as comonads on categories of relational structure…
An invitation to game comonads
Samson Abramsky, Luca Reggio
Game comonads offer a categorical view of a number of model-comparison games central to model theory, such as pebble and Ehrenfeucht-Fraïssé games. Remarkably, the categories of co…
A model category for modal logic
Luca Reggio
We define Quillen model structures on a family of presheaf toposes arising from tree unravellings of Kripke models, leading to a homotopy theory for modal logic. Modal preservation…
Filtral pretoposes and compact Hausdorff locales
Célia Borlido, Panagis Karazeris, Luca Reggio +1
The category of compact Hausdorff locales is a pretopos which is filtral, meaning that every object is covered by one whose subobject lattice is isomorphic to the lattice of filter…
Finitely accessible arboreal adjunctions and Hintikka formulae
Luca Reggio, Colin Riba
Arboreal categories provide an axiomatic framework in which abstract notions of bisimilarity and back-and-forth games can be defined. They act on extensional categories, typically…
Arboreal Categories and Equi-resource Homomorphism Preservation Theorems
Samson Abramsky, Luca Reggio
The classical homomorphism preservation theorem, due to Łoś, Lyndon and Tarski, states that a first-order sentence is preserved under homomorphisms between structures if, and o…
Barr-Exact Categories and Soft Sheaf Representations
Marco Abbadini, Luca Reggio
It has long been known that a key ingredient for a sheaf representation of a universal algebra A consists in a distributive lattice of commuting congruences on A. The sheaf represe…
Polyadic Sets and Homomorphism Counting
Luca Reggio
A classical result due to Lovasz (1967) shows that the isomorphism type of a graph is determined by homomorphism counts. That is, graphs G and H are isomorphic whenever the number…
Lovász-Type Theorems and Game Comonads
Anuj Dawar, Tomáš Jakl, Luca Reggio
Lovász (1967) showed that two finite relational structures A and B are isomorphic if, and only if, the number of homomorphisms from C to A is the same as the number of homomorphism…
Arboreal Categories: An Axiomatic Theory of Resources
Samson Abramsky, Luca Reggio
Game comonads provide a categorical syntax-free approach to finite model theory, and their Eilenberg-Moore coalgebras typically encode important combinatorial parameters of structu…
Model completions for universal classes of algebras: necessary and sufficient conditions
George Metcalfe, Luca Reggio
Necessary and sufficient conditions are presented for the (first-order) theory of a universal class of algebraic structures (algebras) to admit a model completion, extending a char…
A duality theoretic view on limits of finite structures: Extended version
Mai Gehrke, Tomáš Jakl, Luca Reggio
A systematic theory of structural limits for finite models has been developed by Nesetril and Ossona de Mendez. It is based on the insight that the collection of finite structures…
A Cook's tour of duality in logic: from quantifiers, through Vietoris, to measures
Mai Gehrke, Tomas Jakl, Luca Reggio
We identify and highlight certain landmark results in Samson Abramsky's work which we believe are fundamental to current developments and future trends. In particular, we focus on…
Beth definability and the Stone-Weierstrass Theorem
Luca Reggio
The Stone-Weierstrass Theorem for compact Hausdorff spaces is a basic result of functional analysis with far-reaching consequences. We introduce an equational logic asso…
On the axiomatisability of the dual of compact ordered spaces
Marco Abbadini, Luca Reggio
We provide a direct and elementary proof of the fact that the category of Nachbin's compact ordered spaces is dually equivalent to an Aleph_1-ary variety of algebras. Further, we s…
A duality theoretic view on limits of finite structures
Mai Gehrke, Tomáš Jakl, Luca Reggio
A systematic theory of structural limits for finite models has been developed by Nesetril and Ossona de Mendez. It is based on the insight that the collection of finite structures…
A characterisation of the category of compact Hausdorff spaces
Vincenzo Marra, Luca Reggio
We provide a characterisation of the category KH of compact Hausdorff spaces and continuous maps by means of categorical properties only. To this aim we introduce a notion of filtr…
Codensity, profiniteness and algebras of semiring-valued measures
Luca Reggio
We show that, if S is a finite semiring, then the free profinite S-semimodule on a Boolean Stone space X is isomorphic to the algebra of all S-valued measures on X, which are finit…
An open mapping theorem for finitely copresented Esakia spaces
Samuel J. van Gool, Luca Reggio
We prove an open mapping theorem for the topological spaces dual to finitely presented Heyting algebras. This yields in particular a short, self-contained semantic proof of the uni…
Quantifiers on languages and codensity monads
Mai Gehrke, Daniela Petrisan, Luca Reggio
This paper contributes to the techniques of topo-algebraic recognition for languages beyond the regular setting as they relate to logic on words. In particular, we provide a genera…