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 π fibered over a base category π of dimensionless conceptual axes, we show that all empirical laws arise as Cartesian liftings of morphisms in π. The so-called "fundamental constants"ββ,β―c,β―G,β―k_Bβare 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.
https://mystry-geek.blogspot.com/2025/06/the-structure-of-physical-law-as.html