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For an endofunctor $H$ on a hyper-extensive category preserving countablecoproducts we describe the free corecursive algebra on $Y$ as the coproduct ofthe 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 areprecisely 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 somesets $W$ and $Y$.

On Corecursive Algebras for Functors Preserving Coproducts