We present a rigorous categorical framework for modeling creative dynamical processes. We formalize key notions such as ambiguity, inconsistency, and creativity within a mathematical structure that spans theoretical computer science, philosophy of science, and AI/ML. In particular, we introduce the concept of a creative dynamical system as an open-ended category that can extend itself by resolving ambiguities or inconsistencies through the introduction of new morphisms or objects. We connect our formalism to machine learning by suggesting how it could underpin open-ended learning and creativity in intelligent systems.