Representing and Reasoning about time and change is one of the primary issues in the area of Artificial Intelligence (AI) and Knowledge Representation (KR). Despite the importance of time and change in ontology change management process, current ontology researches are based on time- independent models. One of the reasons is that considering time in ontologies can increase the complexity and a comprehensive and very expressive ontology language is needed to represent it. In this paper we propose using state space model along with category theory as a mathematical notation, which is independent of a specific choice of ontology language and any particular implementation to analyze and represent temporal ontological models in the domain of biomedical applications.