Final Coalgebras from Corecursive Algebras

Author Paul Blain Levy

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Paul Blain Levy

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Paul Blain Levy. Final Coalgebras from Corecursive Algebras. In 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 35, pp. 221-237, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


We give a technique to construct a final coalgebra in which each element is a set of formulas of modal logic. The technique works for both the finite and the countable powerset functors. Starting with an injectively structured, corecursive algebra, we coinductively obtain a suitable subalgebra called the "co-founded part". We see—first with an example, and then in the general setting of modal logic on a dual adjunction—that modal theories form an injectively structured, corecursive algebra, so that this construction may be applied. We also obtain an initial algebra in a similar way. We generalize the framework beyond Set to categories equipped with a suitable factorization system, and look at the examples of Poset and Set-op .
  • coalgebra
  • modal logic
  • bisimulation
  • category theory
  • factorization system


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