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The Kechris–Pestov–Todorčević Correspondence from the Point of View of Category Theory

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Abstract

The Kechris–Pestov–Todorčević correspondence (KPT-correspondence for short) is a surprising correspondence between model theory, combinatorics and topological dynamics. In this paper we present a categorical re-interpretation of (a part of) the KPT-correspondence with the aim of proving a dual statement. Our strategy is to take a “direct” result and then analyze the necessary infrastructure that makes the result true by providing a purely categorical proof of the categorical version of the result. We can then capitalize on the Duality Principle to obtain the dual statements almost for free. We believe that the dual version of the KPT-correspondence can not only provide the new insights into the interplay of combinatorial, model-theoretic and topological phenomena this correspondence binds together, but also explores the limits to which categorical treatment of combinatorial phenomena can take us.

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Acknowledgements

The author gratefully acknowledges the financial support of the Ministry of Education, Science and Technological Development of the Republic of Serbia (Grant No. 451-03-68/2020-14/200125).

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Novi Sad, Serbia

    Dragan Mašulović

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  1. Dragan Mašulović
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Correspondence to Dragan Mašulović.

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Communicated by Thomas Streicher.

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Mašulović, D. The Kechris–Pestov–Todorčević Correspondence from the Point of View of Category Theory. Appl Categor Struct 29, 141–169 (2021). https://doi.org/10.1007/s10485-020-09611-z

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  • DOI: https://doi.org/10.1007/s10485-020-09611-z

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