Paolo Perrone (changes) in nLab

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• home page

  personal page

• YouTube channel

• GoogleScholar page

Related nLab pages:

Selected writings

• categorical probability
• monads of probability, measures, and valuations
• Markov category
• category of couplings
• partial evaluation
• weighted category

On category theory:

Introduction to category theory

• Paolo Perrone: Starting Category Theory, World Scientific (2024) [doi:10.1142/13670, arXiv:1912.10642]

• Paolo Perrone, Starting Category Theory, World Scientific, 2024. (website)

On categorical probability theory:

Selected papers

• Tobias Fritz, Paolo Perrone, A Probability Monad as the Colimit of Spaces of Finite Samples, Theory and applications of Categories 34, 2019. (arXiv:1712.05363)

• Tobias Fritz and Paolo Perrone, Stochastic order on metric spaces and the ordered Kantorovich monad, Advances in Mathematics 366, 2020. (arXiv:1808.09898)

• Tobias Fritz, Tomáš Gonda and Paolo Perrone, De Finetti’s theorem in categorical probability. Journal of Stochastic Analysis, 2021. (arXiv:2105.02639)

• Sean Moss and Paolo Perrone, Probability monads with submonads of deterministic states, LICS 2022. (arXiv:2204.07003)

• Carmen Constantin, Tobias Fritz, Paolo Perrone and Brandon Shapiro, Partial evaluations and the compositional structure of the bar construction, Theory and Applications of Categories 39, 2023. (arXiv:2009.07302)

• Sean Moss and Paolo Perrone, A category-theoretic proof of the ergodic decomposition theorem, Ergodic Theory and Dynamical Systems, 2023. (arXiv:2207.07353)

• Paolo Perrone, Markov Categories and Entropy, IEEE Transactions on Information Theory 70(3), 2024. (arXiv:2212.11719)

• Tobias Fritz and Paolo Perrone, A Probability Monad as the Colimit of Spaces of Finite Samples, Theory and applications of Categories 34, 2019. (arXiv:1712.05363)

• Tobias Fritz and Paolo Perrone, Stochastic order on metric spaces and the ordered Kantorovich monad, Advances in Mathematics 366, 2020. (arXiv:1808.09898)

• Tobias Fritz, Tomáš Gonda and Paolo Perrone, De Finetti’s theorem in categorical probability. Journal of Stochastic Analysis, 2021. (arXiv:2105.02639)

• Paolo Perrone and Walter Tholen, Kan extensions are partial colimits, Applied Categorical Structures 30, 2022. (arXiv:2101.04531)

• Sean Moss and Paolo Perrone, Probability monads with submonads of deterministic states, LICS 2022. (arXiv:2204.07003)

• Carmen Constantin, Tobias Fritz, Paolo Perrone and Brandon Shapiro, Partial evaluations and the compositional structure of the bar construction, Theory and Applications of Categories 39, 2023. (arXiv:2009.07302)

• Carmen Constantin, Tobias Fritz, Paolo Perrone and Brandon Shapiro, Weak cartesian properties of simplicial sets, Journal of Homotopy and Related Structures, 2023. (arXiv:2105.04775)

• Sean Moss and Paolo Perrone, A category-theoretic proof of the ergodic decomposition theorem, Ergodic Theory and Dynamical Systems, 2023. (arXiv:2207.07353)

• Paolo Perrone, Markov Categories and Entropy, IEEE Transactions on Information Theory 70(3), 2024. (arXiv:2212.11719)

On Kan extensions:

• Paolo Perrone and Walter Tholen, Kan extensions are partial colimits, Applied Categorical Structures 30, 2022. (arXiv:2101.04531)

On simplicial sets:

• Carmen Constantin, Tobias Fritz, Paolo Perrone and Brandon Shapiro, Weak cartesian properties of simplicial sets, Journal of Homotopy and Related Structures, 2023. (arXiv:2105.04775)

• categorical probability

• monads of probability, measures, and valuations

• Markov category

• category of couplings

• partial evaluation

• weighted category