Induction, Coinduction, and Adjoints
نویسندگان
چکیده
We investigate the reasons for which the existence of certain right adjoints implies the existence of some final coalgebras, and vice-versa. In particular we prove and discuss the following theorem which has been partially available in the literature: let F a G be a pair of adjoint functors, and suppose that an initial algebra F̂ (X) of the functor H(Y ) = X + F (Y ) exists; then a right adjoint G̃(X) to F̂ (X) exists if and only if a final coalgebra Ǧ(X) of the functor K(Y ) = X × G(Y ) exists. Motivated by the problem of understanding the structures that arise from initial algebras, we show the following: if F is a left adjoint with a certain commutativity property, then an initial algebra of H(Y ) = X + F (Y ) generates a subcategory of functors with inductive types where the functorial composition is constrained to be a Cartesian product.
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عنوان ژورنال:
- Electr. Notes Theor. Comput. Sci.
دوره 69 شماره
صفحات -
تاریخ انتشار 2002