The Zhu-Liang Truth Functor Theorem: Truth Necessarily Is a Functor

This paper proposes and proves the Zhu-Liang Truth Functor Theorem: Truth, as the ultimate deterministic law governing the existence and evolution of the universe, must necessarily take the form of a functor. The proof begins with two undeniable meta-facts — the fact of existential difference (F1) and the fact of deterministic correlation (F2) — and reconstructs them in the language of category theory, deriving that truth must be a functor T : S → R from the category S of universal states to a result category R. This functor not only maps states to results but also preserves the causal structure between states. Building on this, we further demonstrate that the process of proof corresponds to a natural transformation between theory categories, and the entire mathematical universe constitutes a dynamic hierarchical network coordinated by functors and natural transformations. The conclusion is fully compatible with G¨odel’s incompleteness theorems and the universe hierarchy of homotopy type theory, providing an ultimate formal foundation for all rational cognition.