It is well known that one can use an adaptation of the inverse-limit construction to solve recursive equations in the category of complete ultrametric spaces.  We show that this construction generalizes to a large class of categories with metric-space structure on each set of morphisms: the exact nature of the objects is less important.  In particular, the construction immediately applies to categories where the objects are ultrametric spaces with 'extra structure', and where the morphisms preserve this extra structure.  The generalization is inspired by classical domain-theoretic work by Smyth and Plotkin.

Our primary motivation for solving generalized recursive metric-space equations comes from recent and ongoing work on Kripke-style models of programming languages with higher-order store in which the sets of worlds must be recursively defined.  We show a series of examples motivated by this line of work.

Joint work with Kristian Stovring and Jacob Thamsborg