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CALCO
2015
Springer

Final Coalgebras from Corecursive Algebras

3 years 7 months ago
Final Coalgebras from Corecursive Algebras
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 .
Paul Blain Levy
Added 17 Apr 2016
Updated 17 Apr 2016
Type Journal
Year 2015
Where CALCO
Authors Paul Blain Levy
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