A novel conceptual framework is developed for the Complexity Levels Theory in a Categorical Ontology of Space, Time and Complex Dynamical Systems. This conceptual and formal construction supports also computer-based ontological studies of emergent biosystems, supercomplex dynamics, evolution and human consciousness. A claim is defended concerning the universal representation of complexity levels in categorical terms in terms of non-commutative diargrams of complex biological relations. As an essential example, the relational-organizational structures of living organisms are represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures that emerge from such relational structures in living systems.
The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations and varying biotopology in speciation and the evolution of species.
