Algebra universalis

, Volume 63, Issue 2–3, pp 243–260 | Cite as

On universal categories of coalgebras

  • Věra Trnková
  • Jiří Sichler


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.

2000 Mathematics Subject Classification

Primary: 08B25 Secondary: 18B15 

Keywords and phrases

categories of coalgebras full embedding universal category 


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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Mathematical Institute of Charles UniversityPraha 8Czech Republic
  2. 2.Department of MathematicsUniversity of ManitobaWinnipegCanada

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