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08/01/2023
Absolute continuity, supports and idempotent splitting in categorical probability
Markov categories have recently turned out to be a powerful high-level f...
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03/24/2023
Weakly affine monads
Introduced in the 1990s in the context of the algebraic approach to grap...
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12/22/2022
Markov Categories and Entropy
Markov categories are a novel framework to describe and treat problems i...
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11/04/2022
Dilations and information flow axioms in categorical probability
We study the positivity and causality axioms for Markov categories as pr...
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07/15/2022
A category-theoretic proof of the ergodic decomposition theorem
The ergodic decomposition theorem is a cornerstone result of dynamical s...
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04/14/2022
Probability monads with submonads of deterministic states - Extended version
Probability theory can be studied synthetically as the computational eff...
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10/13/2021
Lifting couplings in Wasserstein spaces
This paper makes mathematically precise the idea that conditional probab...
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05/06/2021
De Finetti's Theorem in Categorical Probability
We present a novel proof of de Finetti's Theorem characterizing permutat...
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10/14/2020
Representable Markov Categories and Comparison of Statistical Experiments in Categorical Probability
Markov categories are a recent categorical approach to the mathematical ...
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12/23/2019
Notes on Category Theory with examples from basic mathematics
These notes were originally developed as lecture notes for a category th...
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10/09/2019
Probability, valuations, hyperspace: Three monads on Top and the support as a morphism
We consider three monads on Top, the category of topological spaces, whi...
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10/14/2018
Monads, partial evaluations, and rewriting
Monads can be interpreted as encoding formal expressions, or formal oper...
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08/29/2018
Stochastic order on metric spaces and the ordered Kantorovich monad
In earlier work, we had introduced the Kantorovich probability monad on ...
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04/10/2018
Bimonoidal Structure of Probability Monads
We give a conceptual treatment of the notion of joints, marginals, and i...
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12/14/2017
