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Projections of Semilattices in the Language of Category Theory

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Abstract—

This article describes a category theoretic approach to projections of semilattices as an alternative to the classic approach of pattern structure projections. In the special case of Cartesian products and their projections on partial sub-products, this approach forms the basis for a sequential version of the VKF machine learning method that is based on a binary similarity operation.

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ACKNOWLEDGMENTS

The author is grateful to L.A. Yakimova for helpful discussions and to our colleagues at the Dorodnicyn Computing Center of the Russian Academy of Sciences and the Russian State University for the Humanities (especially Prof. E.M. Beniaminov) for their support and constructive discussions. The critical comments and suggestions of Prof. S.O. Kuznetsov were gratefully taken into consideration when preparing the final version of the study.

Funding

This study was supported in part by the Russian Foundation for Basic Research, project no. 18-29-03063mk.

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Authors and Affiliations

  1. Computer Science and Control Federal Research Center, Russian Academy of Sciences, 119333, Moscow, Russia

    D. V. Vinogradov

  2. Russian State University for the Humanities, 125993, Moscow, Russia

    D. V. Vinogradov

Authors
  1. D. V. Vinogradov
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Correspondence to D. V. Vinogradov.

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Translated by A. Ovchinnikova

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Vinogradov, D.V. Projections of Semilattices in the Language of Category Theory. Autom. Doc. Math. Linguist. 55, 89–93 (2021). https://doi.org/10.3103/S0005105521030043

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  • DOI: https://doi.org/10.3103/S0005105521030043

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