Least fixed points in monoidal categories with cartesian structure on objects

Abstract

The paper contains a generalization of the recursion theory in iterative operative spaces. The generalization consists in replacin the partial order in an operative space with arrows in a category. For that purpose the notion of a DM-category is introduced. An example of a DM-category is described which deals with some kind of idealized nontederministic programs together with proofs of the correctness of their work. A theory of fixed points of definable functors in $DM-$categories is developed which contains categorial analogues of all principal results of the abstract recursion theory in iterative operative spaces.