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Corpus ID: 235313650

A Coalgebraic Approach to Dualities for Neighborhood Frames

@article{Bezhanishvili2021ACA,
title={A Coalgebraic Approach to Dualities for Neighborhood Frames},
author={Guram Bezhanishvili and Nick Bezhanishvili and Jim de Groot},
journal={ArXiv},
year={2021},
volume={abs/2106.01628}
}

We develop a uniform coalgebraic approach to Thomason and Jónsson-Tarski type dualities for various classes of neighborhood frames and neighborhood algebras. In the first part of the paper we construct an endofunctor on the category of complete and atomic Boolean algebras that is dual to the double powerset functor on Set. This allows us to show that Thomason duality for neighborhood frames can be viewed as an algebra-coalgebra duality. We generalize this approach to any class of algebras for… Expand

B yabstract Stone duality we mean that the topology or contravariant powerset functor, seen as a self-adjoint exponential Σ (−) on some category, is monadic. Using Beck's theorem, this means that… Expand

Monotonic modal logics form a generalisation of normal modal logics in which the additivity of the diamond modality has been weakened to monotonicity: 3p∨3q → 3(p∨q). This generalisation means that… Expand

Duality results between categories of neighbourhood frames for modal logic and categories of modal algebras (i.e. Boolean algeBRas with an additional unary operation) are presented.Expand