6 papers
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 structu…
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…
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…
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…