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Final Coalgebras from Corecursive Algebras Levy, Paul Blain coalgebra modal logic bisimulation category theory factorization system 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 . Schloss Dagstuhl – Leibniz-Zentrum für Informatik Paul Blain Levy 2015 Is Part Of LIPIcs, Volume 35, 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CALCO.2015.221 urn:nbn:de:0030-drops-55365 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2015.221 eng https://creativecommons.org/licenses/by/3.0/legalcode