In this paper we give a category-theoretic semantics for a simple imperative language featuring unbounded indeterminacy. This semantics satisfies the categorical analogues of continuity and has the meaning of while loops defined as co-limits of $\omega$-diagrams. Furthermore, it collapses via an abstraction function to a semantics that is fully abstract, and coincides with the operational semantics. The abstraction function is the only discontinuous function appearing in our semantics.