Sheaf coherence, self-enrichment, Yoneda

Finite regularity is still local; the next burden is gluing. The ω-germ presheaf satisfies sheaf coherence because local admissible maps agree on refinement-tail overlaps, so the sheaf gluing axiom pastes them without adding external matching data. This gluing result enables self-enrichment: every hom-object

[A,B]

is itself a τ-object, rather than an external collection of arrows. Yoneda then becomes a theorem of the construction — fully faithful and bipolar-preserving — not an imported embedding choice. This is the decisive handoff to Book III: the construction has now earned internal relational sites, and those hom-object loci are exactly what the physical-carrier problem will use as candidates for E_1 localization.