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This talk is part of the Mathematical Phenomenology: Synergies and Connections Workshop of the Bamberg Mathematical Consciousness Science Initiative (BAMΞ): https://www.uni-bamberg.de/en/bamxi/r... The workshop is part of BAMΞ's Mathematical Phenomenology Sprint: https://bamxi.org/research-activities.... Abstract: The nature of the relationships between qualitative aspects of consciousness, or qualia, and their physical substrates remains unclear. The problem of qualia is one of the biggest challenges among the enigmas of consciousness. One difficulty in qualia research is characterization of qualia. Verbal descriptions and simple behavioral responses are unable to capture the richness of qualia, the dilemma faced by the traditional NCC paradigm. Comparing a quale with another quale, however, is not difficult. Such relational characterization of qualia, but now in a structural context, underlies the core of the Qualia Structure paradigm. This new paradigm was inspired by category theory, in particular, the Yoneda lemma, which states that an object in a category is characterized by its relationships to all objects in that category. Inspired by the lemma, the Qualia Structure paradigm proposes a pathway to characterize and organize the structural properties of different qualia type one by one. As a result, it aspires to reach an organizing principle, akin to a Mendeleevian periodic table, for the domains of qualia and their physical substrates. Under this framework, any valid theories of consciousness should link the two domains in a structure-preserving manner. This level of specification and understanding of relations between qualia and the physical would dissolve the Hard Problem of consciousness in its current form. Preprint: https://www.biorxiv.org/content/10.64...