Wellfounded coalgebras
نویسندگان
چکیده
For an endofunctor H an initial algebra I has, by Lambek’s Lemma, invertible structure map, thus, it can be considered as a coalgebra. We call an H-coalgebra wellfounded if it has a coalgebra homomorphism into I. This is equivalent to the wellfoundedness in Taylor’s “Practical Foundations”, defined by means of an induction principle. And it is also equivalent to the recursivity studied by Capretta, Uustalu and Vene: a coalgebra is recursive if it has unique coalgebra-to-algebra homomorphism into every H-algebra. Finally, we also prove that the dual concept of completely iterative algebra is equivalent to wellfoundedness. All these results hold for all endofunctors H preserving preimages.
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