In a 2-category with comma and co-comma squares, 1·f [001V] implies Theorem 1·j [001Z] and Theorem 1·m [0023]; this is true for $\Cat$ and $\Cat^\op$. If we call co-pointwise left lifting (resp., right lifting) in $\Cat$ a pointwise left extension (resp., right extension) in $\Cat^\op$, we have that if in $\Cat$ $\vf : US \To VT$ is exact, then

• (PP) $\vf$ preserves the pointwise left extension under $U$;
• (PP$^*$) $\vf$ preserves the pointwise right extension under $V$;
• (PP$^\op$) $\vf$ preserves the co-pointwise left liftings under $T$;
• (PP$^{*\op}$) $\vf$ preserves the co-pointwise right liftings under $S$.