Point: Self-Referential Structure

Category theory's compositional grammar GCat is the least fixed point of the meta-rule M that sends any essentially algebraic theory to the theory of structure-preserving maps between its models. The same fixed-point architecture — iterate the internal hom from the initial object, take the ω-colimit, invoke Lambek — produces a reflexive object D ≅ D, D in any monoidal closed locally finitely presentable category. This reflexive object is a model of the untyped lambda calculus: universal computation from the Lambek isomorphism alone, no external enumeration required. The monograph builds this result across seven papers: a constructive derivation of category theory from primitives (Elements), the identification of GCat as least fixed point (Grammar), five converging lines of evidence for the fixed-point condition (Computation), the substrate-independent specification identity via D = 1 (Adjunction), the convergence of mathematical and epistemological derivations (Method), and the demonstration that computation is constructively posterior to dimensionality (Dimensionality). A Lean 4 companion (42 files, 0 sorry, 0 custom axioms) verifies the core chain from Adámek's theorem through the lambda calculus model.