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De Finetti’s Construction as a Categorical Limit

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Coalgebraic Methods in Computer Science (CMCS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12094))

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Abstract

This paper reformulates a classical result in probability theory from the 1930s in modern categorical terms: de Finetti’s representation theorem is redescribed as limit statement for a chain of finite spaces in the Kleisli category of the Giry monad. This new limit is used to identify among exchangeable coalgebras the final one.

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Acknowledgements

Staton is supported by a Royal Society Fellowship, and has enjoyed discussions about formulations of de Finetti’s theorem with many people including coauthors on  [18].

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Authors and Affiliations

  1. Institute for Computing and Information Sciences, Radboud University, Nijmegen, NL, The Netherlands

    Bart Jacobs

  2. Department of Computer Science, University of Oxford, Oxford, UK

    Sam Staton

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  1. Bart Jacobs
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  2. Sam Staton
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Correspondence to Bart Jacobs .

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Editors and Affiliations

  1. Université de Paris, CNRS, IRIF, Paris, France

    Daniela Petrişan

  2. Radboud University, Nijmegen, The Netherlands

    Jurriaan Rot

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Jacobs, B., Staton, S. (2020). De Finetti’s Construction as a Categorical Limit. In: Petrişan, D., Rot, J. (eds) Coalgebraic Methods in Computer Science. CMCS 2020. Lecture Notes in Computer Science(), vol 12094. Springer, Cham. https://doi.org/10.1007/978-3-030-57201-3_6

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