Abstract
We construct recursion categories from categories of coalgebras. Let F be a nontrivial endofunctor on the category of sets that weakly preserves pullbacks and such that the category \textbf{Set}_F of F-coalgebras is complete. The category \textbf{Set}_F may be embedded in the category \mathbf{Pfn}_F of F-coalgebras and partial morphisms, which is a P-category that is prodominical but not dominical in general. An existence theorem of A. Heller is applied to certain subcategories of \textbf{Pfn}_F to obtain examples of recursion categories of coalgebras.