  O-categories generalize categories of domains to provide just the structure
required to compute fixed points of locally continuous functors. Parametrized
fixed points are of particular interest to denotational semantics and are often
given by "dagger operations". We generalize existing techniques to define a
functorial dagger operation on locally continuous functors between
O-categories. We show that this dagger operation satisfies the Conway
identities, a collection of identities used to axiomatize iteration theories.
We study the behaviour of this dagger operation on natural transformations and
consider applications to semantics of session-typed languages.
