Abstract
This paper develops a categorical foundation for teleparallel gravity by uniting the structural, dynamical, equivalence, and intelligence aspects of torsion within a functorial framework, as quantitatively detailed in the paper, A Unified Gauge Connection with Quantum Torsion in a Teleparallel Geometry. The teleparallel connection is reformulated as a functorial lift between the categories of inertial geometry and physical force, in which torsion plays the role of a nontrivial 2-morphism and the inertial constant ת acts as the natural scaling morphism between geometric and dynamical domains. We show that the Weitzenböck and Levi-Civita connections are naturally equivalent functors on the category of frame bundles, with contortion representing their connecting natural transformation. The resulting formulation renders the teleparallel field equations as functorial invariants and identifies the equivalence principle itself as a categorical isomorphism between curvature and torsion based descriptions of gravitation. An extension introduces the integrative morphism of intelligence as a self-consistent principle of directed coherence, bridging geometry and cognition. Together these elements provide the categorical groundwork for a quantum–intelligent continuum of teleparallel gauge geometry.
Categorical-Foundations-of-Teleparallel-Gauge-Geometry-Structure-Dynamics-Equivalence-and-Intelligence-1