The qualitative nature of our conscious experiences, though routinely acknowledged, has rarely been explicitly modeled simply because we did not have a mathematical definition of the notion of quality. Recently, as part of the axiomatization of cohesion, F. William Lawvere defined QUALITY. Based on Lawvere's definition of quality, we formalized qualia space as a categorical product of qualities. Our manuscript, to the best of our knowledge, is the first paper to apply the category theory of quality and cohesion to formalize the binding of qualitative qualia into the unity of consciousness. As such, we are confident that our work will inspire further in-depth mathematical investigations of the categorical product of qualities as a model of the qualia space.