In the passage from the Fukaya category to the derived category, the morphism space only retains $HF^{0}$, not the full $HF^{*}$. The ususal way the derived category remembers higher Floer cohomology, is via the shift operator $[m]$. However, in the Thomas-Yau-Joyce picture, working with the almost calibrated setting means conjecturally that we are picking out an abelian subcategory, which breaks the shift symmetry of the derived category. This gives a categorical explanation why $HF^{0}$ may behave very differently from the higher Floer groups.