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On universal categories of coalgebras

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Abstract

A category \({\mathcal{K}}\) is called universal if for every accessible functor F : Set → Set the category of all F-coalgebras and the category of all F-algebras can be fully embedded into \({\mathcal{K}}\). We prove that for a functor G preserving intersections, the category Coalg G of all G-coalgebras is universal unless the functor G is linear, that is, of the form GX = X × A + B for some fixed sets A and B. Other types of universality are also investigated.

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Authors and Affiliations

  1. Mathematical Institute of Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

    Věra Trnková

  2. Department of Mathematics, University of Manitoba, Winnipeg, R3T 2N2, Canada

    Jiří Sichler

Authors
  1. Věra Trnková
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  2. Jiří Sichler
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Corresponding author

Correspondence to Jiří Sichler.

Additional information

Presented by J. Adámek.

The first author gratefully acknowledges the support of MSM 0021620839, a project of the Czech Ministry of Education. The second author gratefully acknowledges the support provided by the NSERC of Canada.

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Trnková, V., Sichler, J. On universal categories of coalgebras. Algebra Univers. 63, 243–260 (2010). https://doi.org/10.1007/s00012-010-0077-0

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  • DOI: https://doi.org/10.1007/s00012-010-0077-0

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