Kleisli morphisms and randomized congruences for the Giry monad (Q995624)
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scientific article; zbMATH DE number 5186654
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Kleisli morphisms and randomized congruences for the Giry monad |
scientific article; zbMATH DE number 5186654 |
Statements
Kleisli morphisms and randomized congruences for the Giry monad (English)
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3 September 2007
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The present paper is about the Kleisli morphisms in the Giry monad (proposed and investigated by \textit{M. Giry} [Lect. Notes Math. 915, 68--85 (1981; Zbl 0486.60034)] as one component for the categorical foundation of probability theory) and their associated morphisms and congruences. The relationship between kernels of these morphisms and congruences is explained, and a unique factorization of a morphism through this kernel is shown to exist. This study is based on a subdivision into countably generated equivalence relations on the space of all subprobabilities; operations on these relations are investigated quite closely.
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Kleisli morphisms
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Giry monad
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Hennessy-Milner logic
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stochastic relations
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randomized
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