Suppose $F$ is a fully faithful functor from abelian category $A$ to abelian category $B$, then $F$ induces a derived functor $DF$ between their derived categories, \begin{equation} DF:D^*A \rightarrow D^* B \end{equation} where $*$ could be -, +, b, $\emptyset$. When is $DF$ also fully faithful and when it is not fully faithful?
2026-03-26 22:15:06.1774563306
Breaking down of fully faithfulness when taking its derived functor?
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