Let $A$ and $B$ be two abelian categories. Assume that there exist a functor $F$ between them which is exact, full and essencially surjective.
If $x$ is a projective object in $A$, then $F(x)$ is a projective object in $B$?
Let $A$ and $B$ be two abelian categories. Assume that there exist a functor $F$ between them which is exact, full and essencially surjective.
If $x$ is a projective object in $A$, then $F(x)$ is a projective object in $B$?