Enriched category as a model of qualia structure based on similarity judgements.

Qualitative relationships between two instances of conscious experiences can be quantified through the perceived similarity. Previously, we proposed that by defining similarity relationships as arrows and conscious experiences as objects, we can define a category of qualia in the context of category theory. However, the example qualia categories we proposed were highly idealized and limited to cases where perceived similarity is binary: either present or absent without any gradation. Here, we introduce enriched category theory to address the graded levels of similarity that arises in many instances of qualia. Enriched categories generalize the concept of a relation between objects as a directed arrow (or morphism) in ordinary category theory to a more flexible notion, such as a measure of distance. As an alternative relation, here we propose a graded measure of perceived dissimilarity between the two objects. We claim that enriched categories accommodate various types of conscious experiences. An important consequence of this claim is the application of the Yoneda lemma in enriched category; we can characterize a quale through a collection of relationships between the quale and the other qualia up to an (enriched) isomorphism.