# Probability, valuations, hyperspace: Three monads on Top and the support as a morphism

@article{Fritz2019ProbabilityVH, title={Probability, valuations, hyperspace: Three monads on Top and the support as a morphism}, author={Tobias Fritz and Paolo Perrone and Sharwin Rezagholi}, journal={ArXiv}, year={2019}, volume={abs/1910.03752} }

We consider three monads on Top, the category of topological spaces, which formalize topological aspects of probability and possibility in categorical terms. The first one is the hyperspace monad H, which assigns to every space its space of closed subsets equipped with the lower Vietoris topology. The second is the monad V of continuous valuations, also known as the extended probabilistic powerdomain. Both monads are constructed in terms of double dualization. This not only reveals a strong… Expand

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