What is the nature of the relationship between qualia, or contents of consciousness, and behavioral reports? Traditionally, this type of question has been only addressed via a qualitative and philosophical approach. Some theorists emphasize an incomplete and inaccurate nature of reports of one’s own qualia to discourage formal research programs on qualia. Other empirical researchers, however, have made substantial progress in understanding the structure of qualia from such limited reports. What is the precise relationship between the two? To answer this question, we introduce a concept of “adjoint” or “adjunction” from category theory in mathematics. We claim that adjunction captures many aspects of the nuanced relationships between qualia and reports. A concept of adjunction allows us to clarify various conceptual issues with precise mathematical formulation. More importantly, an idea of adjunction naturally leads to various proposals of new empirical experiments to test predictions about the nature of their relationship.