We present a concise but rigorous formulation of Coulon Enrichment Functors, a categorical framework unifying geometric, symplectic, quantum, and combinatorial structures under a single functorial spine Γ̂.

The framework emphasizes computability, topological coherence, and dynamical consistency, enforced through explicit structural conditions.

We formalize enrichment via symplectic signatures, define functorial transitions, and provide proofs using hypothetical syllogisms, homotopy arguments, and contextual (“topetic”) logic. Applications range from discrete computation and sorting to economic dynamics and stability prediction.

Abstract

We present a concise but rigorous formulation of Coulon Enrichment Functors, a categorical framework unifying geometric, symplectic, quantum, and combinatorial structures under a single functorial spine Γ̂. 

The framework emphasizes computability, topological coherence, and dynamical consistency, enforced through explicit structural conditions. 

We formalize enrichment via symplectic signatures, define functorial transitions, and provide proofs using hypothetical syllogisms, homotopy arguments, and contextual (“topetic”) logic. Applications range from discrete computation and sorting to economic dynamics and stability prediction.