Strategy

We have two dualities: defined versus undefined and object versus morphism. Call these dualities epistemic and ontic, respectively.

In which cases can the dualities be related and finessed, i.e. in which cases can we use defined/undefined to study object/morphism? Exactly when we can expect a sharp separation between objects (stuff) and morphisms (acts)? Or exactly when we cannot? When we assume a sharp distinction, let us call that assumption Abelian.

In the provisional formalism, note that the Abelian assumption is something that holds between $$R_m$$ and $$R^n$$.