Why reconstruction descent is not supplied by a path sum

For completeness, one elementary compatibility statement from the analytic comparison can be restated and proved without constructing its absent graph.

Let

be a linear reconstruction of presentations. A candidate later map $\tilde{M}:\mathcal{P}\to {\mathcal{D}}^{\prime }(W)$ acts intrinsically on reconstructed kernels only if it respects every reconstruction identity.