Kleisli categories and probability - 02 - The Kleisli category of a monad
Channel: Arthur Parzygnat
Date: 2020-03-19

This video introduces the Kleisli category associated to a monad. Given a monad on a category, one can construct a new category that has the same objects as the original category but whose morphisms are slightly different. A morphism from X to Y in the Kleisli category is a morphism from X to P(Y) in the original category, where P is the functor from the monad. In the case of the Giry monad, such morphisms correspond to Markov kernels. The statement made at the end of a video is a relatively recent result by Abraham Westerbaan (https://arxiv.org/abs/1501.01020). 

This video is part of the playlist on Categorical probability theory: https://www.youtube.com/playlist?list=PLSx1kJDjrLRSKKHj4zetTZ45pVnGCRN80

The next video in this series is on Markov kernels: https://youtu.be/psUDrasc21o

The previous video in this series is on The Giry monad: https://youtu.be/5t1FN_v7dB8

These videos were created during the 2019 Spring/Summer semester at the UConn CETL Lightboard Room.