Conscious experience has five essential properties—intrinsicality, information, integration, exclusion, and composition—as proposed by Integrated Information Theory (IIT), but the necessity of these axioms is unclear due to their informal presentation and dependence on a specific mathematical model. A category-theoretic approach, a meta-mathematical framework for making relations between formal structures precise, organizes these five properties around a smaller number of meta-mathematical principles. Category theory characterizes structures by universal mapping properties, a unique-existence condition for all instances. This suggests that the axioms for consciousness correspond to universal mapping properties, leading to the idea that consciousness is a universal property.
Perceived similarity between conscious experiences can be quantified, and category theory offers a framework for modeling these relationships. Earlier work treated similarity as binary—either present or absent—but many experiences involve graded levels of similarity. This paper introduces enriched category theory, which replaces binary arrows with more flexible relations, such as a measure of perceived dissimilarity. The authors argue that enriched categories can accommodate various types of conscious experiences. A key implication is that the Yoneda lemma in enriched category theory allows a quale to be characterized by its collection of relationships to other qualia, up to an enriched isomorphism.
The relationship between qualia (subjective experiences), the contents of consciousness, and behavioral reports is examined through the lens of category theory, specifically the mathematical concept of adjunction. While some theorists argue that reports of one's own qualia are inherently incomplete and inaccurate, hindering formal research, empirical researchers have still made progress in understanding qualia structure from such reports. The authors propose that adjunction captures nuanced aspects of this relationship, establishing coherence between two categories that are not equivalent but importantly related. This mathematical formulation clarifies conceptual issues and suggests new empirical experiments to test predictions about qualia and reports, advancing consciousness research.