## View abstract

### Session S27 - Categories and Topology

Thursday, July 15, 12:30 ~ 13:00 UTC-3

## The Double Category of Measurable Functions and Stochastic Maps

### Evangelia Aleiferi

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The category of measurable spaces and stochastic maps, $\mathbf{Stoch}$, was introduced by Giry in 1982, following some highly referenced unpublished manuscripts by Lawvere back in 1962. Giry was able to show that the Kleisli category of the Giry monad on the category of measurable functions $\mathbf{Meas}$, is exactly the same as the category $\mathbf{Stoch}$. This shows that $\mathbf{Stoch}$ behaves for $\mathbf{Meas}$ as the category $\mathbf{Rel}$ behaves for the category $\mathbf{Set}$. Inspired by this, and the advantages of combining relations and functions into one structure, that of the double category of sets, relations horizontally, and functions vertically, we are defining the double category of measurable spaces, stochastic maps horizontally, and measurable functions vertically. In this talk we will explore some of the properties of this double category.