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Logical Construction of Final Coalgebras

Luigi Santocanale
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Abstract

We prove that every finitary polynomial endofunctor of a category $C$ has a final coalgebra if $C$ is locally Cartesian closed, has finite disjoint coproducts and a natural number object. More generally, we prove that the category of coalgebras for such an endofunctor has all finite limits.

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Luigi Santocanale. 2004-03-14. Logical Construction of Final Coalgebras. https://arxiv.org/abs/math/0403227

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