My question is the following:
Let $T$ be a topos and $X\to e$ be a covering of the final object $e\in T$ with respect to the canonical topology. We have a morphism of topoi $f\colon T/X\to T$ where $f^\star F=F\times X$ for $f\in T$. Now Martin Olsson claims in Algebraic Spaces and Stacks in Lemma 2.4.18 that to check that a given morphism of complexes of Sheaf of modules in $T$ is quasi-isomorphism, it suffices to show that it becomes a quasi-isomorphism after pulling back to $T/X$.
Could anyone tell me what he means by that and why it is true? Many thanks in advance.