Categorical Structures as Generative Geometry: A Unified Model of Duality, Thickness, EM/Kleisli Layers, ∞‑Stratification, and Curvature

Abstract

This paper presents a generative geometric interpretation of categorical structures, where dualization forms layered depth, monads and comonads create thickness, EM/Kleisli yield four-layer organization, and ∞-categorical stratification and curvature describe higher-order deviations in generative processes.