25 citations · 61 across the 22 of their papers we have counts for
11 papers · 1 filter
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…
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…
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…
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…
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…
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…
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…
The Schützenberger product for syntactic spaces
Mai Gehrke, Daniela Petrisan, Luca Reggio
Starting from Boolean algebras of languages closed under quotients and using duality theoretic insights, we derive the notion of Boolean spaces with internal monoids as recognisers…