Characterizing consciousness in and of itself is notoriously difficult. Any effort to define consciousness seems to evade what it tries to achieve. In particular, definitions often involve comparisons of different kinds of “consciousness” in a self-referential manner. The tautological nature of characterizing consciousness has led some scholars to propose that establishing a science of consciousness is infeasible. Here, we propose an alternative approach to characterize, and to eventually define, consciousness through exhaustive descriptions of consciousness’ relationships to all other consciousness. This approach is mathematically founded in category theory. Indeed, category theory can prove two objects A and B in a category can be equivalent if and only if all the relationships that A holds with others in the category are the same as those of B; this proof is called the Yoneda lemma. To introduce the Yoneda lemma, we gradually introduce key concepts of category theory to consciousness researchers in this paper. Along the way, we propose several possible definitions of categories of consciousness, both in terms of level and contents, through the usage of simple examples. We also propose empirical research programs that can test the validity of our proposed categories of consciousness and to improve them. We propose to use the categorical structure of consciousness as a gold standard if one tries to empirically test some structural theories of consciousness, such as Integrated Information Theory of consciousness. <<<