AbstractProbabilities 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
International audienceThis paper describes some basic relationships between mathematical structures ...
International audienceThe monad of convex sets of probability distributions is a well-known tool for...
The monad of convex sets of probability distributions is a well-known tool for modelling the combina...
Probabilities are understood abstractly as forming a monoid in the category of effect algebras. They...
Probabilities are understood abstractly as forming a monoid in the category of effect algebras. They...
Probabilities are understood abstractly as forming a monoid in the category of effect algebras. They...
Probabilities are understood abstractly as forming a monoid in the category of effect algebras. They...
Probabilities are understood abstractly as forming a monoid in the category of effect algebras. They...
Probabilities are understood abstractly as forming a monoid in the category of effect algebras. They...
AbstractProbabilities are understood abstractly as forming a monoid in the category of effect algebr...
The following full text is a preprint version which may differ from the publisher's version
Abstract. State spaces in probabilistic and quantum computation are convex sets, that is, Eilenberg–...
Abstract. State spaces in probabilistic and quantum computation are convex sets, that is, Eilenberg–...
This paper describes some basic relationships between mathematical structures that are relevant in q...
International audienceThis paper describes some basic relationships between mathematical structures ...
International audienceThis paper describes some basic relationships between mathematical structures ...
International audienceThe monad of convex sets of probability distributions is a well-known tool for...
The monad of convex sets of probability distributions is a well-known tool for modelling the combina...
Probabilities are understood abstractly as forming a monoid in the category of effect algebras. They...
Probabilities are understood abstractly as forming a monoid in the category of effect algebras. They...
Probabilities are understood abstractly as forming a monoid in the category of effect algebras. They...
Probabilities are understood abstractly as forming a monoid in the category of effect algebras. They...
Probabilities are understood abstractly as forming a monoid in the category of effect algebras. They...
Probabilities are understood abstractly as forming a monoid in the category of effect algebras. They...
AbstractProbabilities are understood abstractly as forming a monoid in the category of effect algebr...
The following full text is a preprint version which may differ from the publisher's version
Abstract. State spaces in probabilistic and quantum computation are convex sets, that is, Eilenberg–...
Abstract. State spaces in probabilistic and quantum computation are convex sets, that is, Eilenberg–...
This paper describes some basic relationships between mathematical structures that are relevant in q...
International audienceThis paper describes some basic relationships between mathematical structures ...
International audienceThis paper describes some basic relationships between mathematical structures ...
International audienceThe monad of convex sets of probability distributions is a well-known tool for...
The monad of convex sets of probability distributions is a well-known tool for modelling the combina...