by
Bart Jacobs

Citations: | 1 - 1 self |

@MISC{Jacobs_probabilities,distribution,

author = {Bart Jacobs},

title = {Probabilities, Distribution Monads, and Convex Categories},

year = {}

}

Probabilities are understood abstractly as forming a monoid in the category of effect algebras. They can be added, via a partial operation, and multiplied. This generalises key properties of the unit interval [0, 1]. Such effect monoids can be used to define a probability distribution monad, again generalising the situation for [0, 1]-probabilities. It will be shown that there are translations back-and-forth, in the form of an adjunction, between effect monoids and “convex ” monads. This convexity property is formalised, both for monads and for categories. In the end this leads to “triangles of adjunctions ” (in the style of Coumans and Jacobs) relating all the three relevant structures: probabilities, monads, and categories. 1

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