2 citations · 4 across the 11 of their papers we have counts for
12 papers
A topological proof that compact Hausdorff spaces are not finitely co-concrete
Marco Abbadini
Lieberman, Rosický, and Vasey proved that - the opposite of the category of compact Hausdorff spaces - is not finitely concrete by a route through…
A topos for étale-finite Heyting algebras
Marco Abbadini, Rodrigo Nicolau Almeida, Igor Arrieta
A longstanding open problem is whether every Heyting algebra is the lattice of truth values (i.e., of subterminal objects) of some elementary topos. A positive answer is known for…
Unital Specker -groups and boolean multispaces
Marco Abbadini, Daniele Mundici
As a topological generalization of the notion of a multiset, a boolean multispace is a boolean space with a continuous function , where $\mathbb Z_…
On the symmetry behind duality
Marco Abbadini, Achim Jung
Dualities such as Stone duality and the duality between sober spaces and spatial frames hinge on an interaction between open sets and compact saturated sets. In several important c…
On the lack of colimits in various categories arising in pointfree topology and algebraic logic
Marco Abbadini, Guram Bezhanishvili, Luca Carai
We prove that the category of McKinsey-Tarski algebras is not equivalent to a variety of algebras, thus answering a question of Peter Jipsen in the negative. More generally, we sho…
Duality for finitely valued algebras
Marco Abbadini, Adam Přenosil
The theory of natural dualities provides a well-developed framework for studying Stone-like dualities induced by an algebra which acts as a dualizing object when equip…
Vietoris endofunctor for closed relations and its de Vries dual
Marco Abbadini, Guram Bezhanishvili, Luca Carai
We generalize the classic Vietoris endofunctor to the category of compact Hausdorff spaces and closed relations. The lift of a closed relation is done by generalizing the construct…
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…
MacNeille completions of subordination algebras
Marco Abbadini, Guram Bezhanishvili, Luca Carai
-subordination algebras are a natural generalization of de Vries algebras. Recently it was proved that the category of -subordination a…
A generalization of de Vries duality to closed relations between compact Hausdorff spaces
Marco Abbadini, Guram Bezhanishvili, Luca Carai
Stone duality generalizes to an equivalence between the categories of Stone spaces and closed relations and of boolean algebr…
Operations that preserve integrability, and truncated Riesz spaces
Marco Abbadini
For any real number , we characterise the operations that preserve -integrability, i.e., the operations under which, for every me…
Dedekind sigma-complete l-groups and Riesz spaces as varieties
Marco Abbadini
We prove that the category of Dedekind -complete Riesz spaces is an infinitary variety, and we provide an explicit equational axiomatization. In fact, we show that finitely many…