Presentations and actual kernels

Let ${\mathcal{P}}_{\mathrm{int}}$ denote the finite direct sum of the internal coefficient presentation spaces. Its reconstruction map, including summation into the common tensor-valued kernel, is

Thus

This is a space of already defined internal distributions.

On $U_{\mathrm{can}}$, canonical contraction gives a linear map

Every identity between reconstructed kernels is respected by this canonical map on its proved domain.