Characterizing consciousness directly is notoriously difficult. This paper proposes an alternative approach: defining consciousness through its relationships to all other consciousness, using category theory. The Yoneda lemma proves that two objects in a category are equivalent if and only if all their relationships to others are identical. The authors introduce key category theory concepts for consciousness researchers and propose several possible definitions of categories of consciousness, in terms of level and contents, using simple examples. They suggest using the categorical structure of consciousness as a gold standard to formalize empirical research, such as color qualia structure at fovea and periphery, and to empirically test theories of consciousness.
A mathematical framework called category theory (CT) can formally define and study the relationship between consciousness and its neural substrates. CT uses concepts such as category, inclusion functor, expansion functor, and natural transformation, each mapped to specific features in the neural correlates of consciousness (NCC). Applying CT to integrated information theory (IIT) and the temporospatial theory of consciousness (TTC) shows that natural transformation reveals the need to go beyond NCC and raises questions that any future neuroscientific theory of consciousness must address.