A Topological and Group-Theoretic Framework for Linking Chemical and Biological Systems

This paper presents a mathematical framework that unifies chemical and biological organization through topological and algebraic principles. The model embeds a small category 𝒞DNA as the core algebraic structure within a continuous topological manifold representing permissible chemical and biological transformations. This structure establishes a correspondence between molecular complementarity, polarity inversion, and other binary operations in biology, providing a formal mathematical bridge between the domains of chemistry and biology. The framework aims to offer a rigorous foundation for representing biological symmetry and constraint in a manner consistent with both physical and algebraic laws.