17.3.3 Program C: functorial transport

17.3.3 Program C: functorial transport

The finite transport theorem in Chapter 16 gives sufficient conditions for exact reuse, while its transport defects describe partial reuse. The open problem is to characterize the maximal substructure on which coverage, semantic, observer, and admission defects vanish across an admitted family of environment morphisms. This is the infinite persistence core of Chapter 16.

A useful target is a persistence comparison theorem. It should relate relearning after transport to transporting the learned colimit and identify the failure of that comparison precisely with the registered transport defect. Compactness or accessibility of knowledge objects, completeness of the relevant subobject lattices, continuity of transport, and control of cumulative observer and tangent defects are candidate hypotheses. None alone guarantees that the infinite core is nontrivial.