The Structure of Physical Law as a Grothendieck Fibration

Abstract
We present a categorical framework for understanding the emergence of physical law from measurement. By modeling physical quantities as objects in a total category 𝓔 fibered over a base category 𝓑 of dimensionless conceptual axes, we show that all empirical laws arise as Cartesian liftings of morphisms in 𝓑. The so-called "fundamental constants"—ℏ, c, G, k_B—are revealed to be cocycle data, or connection coefficients, ensuring coherence under changes of unit systems. Our framework elevates metrology to its proper foundational role: not just supporting physics, but structuring its very possibility.

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