Naturality

Naturality is the principle that a transformation should be independent of arbitrary representation choices. It should commute with the structure-preserving maps between representations.

Informally, naturality asks whether the same conceptual operation behaves consistently across equivalent presentations of the same idea.

In categorical terms, a natural transformation relates functors in a way that makes the relevant diagrams commute:

F(A) -> G(A)
 |       |
 v       v
F(B) -> G(B)

In modeling terms, naturality asks:

Does this transformation depend on accidental representation details?
If a value, observation, event, or entity is represented differently, does the transformation still mean the same thing?
Does serialization, projection, reconstitution, validation, or realization commute with the relevant mappings?
Are special cases breaking a claimed abstraction?

Examples:

A value transform should not depend on whether the value is dictionary-backed, layout-buffer-backed, or columnar, unless representation is explicitly part of the boundary.
Reconstitution should produce semantically equivalent observations from different persisted representations when those representations are intended to be equivalent.
A projection should preserve its declared meaning across schema, storage, or transport changes.
Realization should preserve observer, entity, transition, and boundary meaning across runtime choices.

Naturality is useful for detecting hidden coupling. If a model says two representations are equivalent but an operation behaves differently for one of them, the operation is not natural with respect to that equivalence.