  We define a framework for incorporating alternation-free fixpoint logics into
the dual-adjunction setup for coalgebraic modal logics. We achieve this by
using order-enriched categories. We give a least-solution semantics as well as
an initial algebra semantics, and prove they are equivalent. We also show how
to place the alternation-free coalgebraic $\mu$-calculus in this framework, as
well as PDL and a logic with a probabilistic dynamic modality.
