"We say that $F$ is half-full if for any pair of objects $X,Y \in \mathcal{C}$ such that $F(X)$ and $F(Y)$ are isomorphic in $\mathcal{C}'$, there exists an isomorphism $X \simeq Y$ in $\mathcal{C}$."
M. Kashiwara and P. Schapira, "Categories and sheaves", Grundlehren der Mathematischen Wissenschaften 332, Springer-Verlag, Berlin, 2006.
no subject
M. Kashiwara and P. Schapira, "Categories and sheaves", Grundlehren der Mathematischen
Wissenschaften 332, Springer-Verlag, Berlin, 2006.