Enriched Bicategorical and Yoneda Theoretic Framework for Relational Quantum Dynamics (RQD)

Relational Quantum Dynamics (RQD) provides a category-theoretic relational interpretation of quantum mechanics, treating quantum interactions as intrinsically observer-dependent. This paper extends RQD’s categorical framework by incorporating enriched and higher-category structures to capture quantitative information metrics and multi-agent relationality. We introduce an enriched category formulation of RQD in which the functorial mapping F : Q → A (from physical quantum processes to awareness updates) carries information- theoretic weights—specifically quantum mutual information I(A : B) and integrated information Φ—as morphism annotations. We further propose a bicategorical structure for RQD to model multiple interacting observers, introducing 2-morphisms to represent bidirectional awareness updates in multi-agent scenarios. Using the Yoneda Lemma, we formalize RQD’s relational ontology, which is an object’s identity is characterized entirely by its morphisms (relationships) to other objects, aligning with the principle that quantum states have no absolute properties outside of interactions. We show how an “awareness” metric A(A : B), combining I(A : B) and Φ, can be systematically embedded in the categorical formalism—either as an enrichment of hom-sets or as additional functorial data—thereby making agents’ awareness updates explicitly quantitative. These extensions yield a richer mathematical model of RQD that can handle complex multi-observer setups and quantify the degree of relational awareness in each interaction. We discuss potential implications of this extended framework, challenges in formalizing consciousness within quantum theory, and avenues for further research, including experimental considerations and links to broader category-theoretic quantum foundations.