Effect pullback

For example, if $T={\mathrm{Tr}}_{\mathrm{r}}$ and ${\Pi }_w=E_w\otimes I_{\mathrm{r}}$, compatibility is exact because $T^{\ast }(E)=E\otimes I_{\mathrm{r}}$. Readout at another time must first be pulled back through the appropriate evolution; a label aggregation is not an evolution map.