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math.GN2023
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…
math.LO2023
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…