Probabilities, distribution monads, and convex categories

B.P.F. Jacobs

Research output: Contribution to journalArticleAcademicpeer-review

19 Citations (Scopus)

Abstract

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 generalizes key properties of the unit interval [0,1]. Such effect monoids can be used to define a probability distribution monad, again generalizing 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 formalized, 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.
Original languageEnglish
Pages (from-to)3323-3336
JournalTheoretical Computer Science
Volume412
Issue number28
DOIs
Publication statusPublished - 2011

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