A Categorical Framework for Dimensioned Quantities and Unit Systems with an Application to Electromagnetics

This letter introduces a categorical framework in which electrical quantities are modeled as elements of a fixed D-graded commutative ℝ-algebra, and concrete unit systems are realized as choices of homogeneous base quantities in a corresponding TD-algebra. Within this framework, changes of unit system for a fixed dimension group D are represented by graded TD-algebra automorphisms that capture SI-CGS conversions such as the MKSA-rCGS-emu current transformation. As a practical contribution to electrical engineering, we derive a dimensionless relation between MKSA and rCGS-emu current units that ensures the invariance of all dimensionless electrical observables under SI-CGS unit changes.