We propose a categorical formulation of renormalization in which scale changes are encoded as functors between categories (or topoi) that represent physical models at distinct resolution scales. Renormalization is presented as a coherent family of functors Rs→t between scale-categories Cs and Ct (for ultraviolet s towards infrared t), equipped with natural transformations encoding coarse-graining maps and the algebra of observables’ projection. Under mild completeness hypotheses we conjecture the existence of universal fixed objects — categorical RG fixed points — characterized by limit/colimit universality. Diagrammatic examples illustrate the finite-lattice → continuum passage. Consequences for photonic RG flow and connections to recent photonics/G-Theory studies are indicated and testable toy-model checks are suggested. This work aims to bridge categorical methods and renormalization practice, with particular eye toward photonic theories and De Ceuster’s G-Theory diagnostics.