Induction, Coinduction, and Adjoints

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 G be a pair of adjoint functors, and suppose that an initial algebra F(X) of the functor H(Y ) = X + F(Y ) exists; then a right adjoint G(X) to F(X) exists if and only if a final coalgebra G(X) of the functor K(Y ) = X

• Type: Journal
• Year: 2002
• Where: ENTCS
• Authors: J. Robin B. Cockett, Luigi Santocanale
• Keywords: ENTCS 2002, Final Coalgebra, Functors, Initial Algebra