• Corpus ID: 108285178

A Probability Monad as the Colimit of Spaces of Finite Samples

  title={A Probability Monad as the Colimit of Spaces of Finite Samples},
  author={Tobias Fritz and Paolo Perrone},
  journal={arXiv: Probability},
We define and study a probability monad on the category of complete metric spaces and short maps. It assigns to each space the space of Radon probability measures on it with finite first moment, equipped with the Kantorovich-Wasserstein distance. This monad is analogous to the Giry monad on the category of Polish spaces, and it extends a construction due to van Breugel for compact and for 1-bounded complete metric spaces. We prove that this Kantorovich monad arises from a colimit construction… 
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