Natural Transformation η

Definition

The upgrade map embedding an institutional system into its regenerative counterpart. ⚠️ Calling it a NATURAL transformation is a condition, not a consequence: naturality reduces to a substantive compatibility requirement — that upgrading commutes with structural redesign — and it is the honest statement of what "regeneration is architecture-invariant" would mean. The source asserts the conclusion. What is worth proving is stronger: that the upgrade map is UNIVERSAL, so every morphism from a system into a regenerative one factors uniquely through it. That would make the regenerative form canonical rather than one option among many, and it is stated rather than discharged.

Formula

Example

η_hospital embeds a traditional budget-cycle hospital into its PSC-governed, RCA-aligned regenerative version. The natural transformation describes how any institution can be systematically upgraded.

Source

FRS Section 4.5