Toward a Category Theory Design of Ontological Knowledge Bases

I discuss (ontologies_and_ontological_knowledge_bases / formal_methods_and_theories) duality and its category theory extensions as a step toward a solution to Knowledge-Based Systems Theory. In particular I focus on the example of the design of elements of ontologies and ontological knowledge bases of next three electronic courses: Foundations of Research Activities, Virtual Modeling of Complex Systems and Introduction to String Theory.Comment: 10 pages, Preliminary results to International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management (IC3K 2009