Recursion categories of coalgebras

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 ${\text{Set}}_F$ of $F$-coalgebras is complete. The category ${\text{Set}}_F$ 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 ${\text{Pfn}}_F$ to obtain examples of recursion categories of coalgebras.

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