  For an endofunctor $H$ on a hyper-extensive category preserving countable
coproducts we describe the free corecursive algebra on $Y$ as the coproduct of
the final coalgebra for $H$ and the free $H$-algebra on $Y$. As a consequence,
we derive that $H$ is a cia functor, i.e., its corecursive algebras are
precisely the cias (completely iterative algebras). Also all functors $H(-) +
Y$ are then cia functors. For finitary set functors we prove that, conversely,
if $H$ is a cia functor, then it has the form $H = W \times (-) + Y$ for some
sets $W$ and $Y$.
