I was reading the lecture notes of Pierre Schapira
http://www.math.jussieu.fr/~schapira/lectnotes/AlTo.pdf I am not able to understand one thing. Please help. In page 75, theorem 4.6.1, the author says that 'quasi-isomorphism from X to $\lambda(X)$ is functorial in C. What does it mean. What does isomorphism functorially mean in general? Please help.
It means that given a morphism $f : X \rightarrow Y$, the diagram $$\require{AMScd} \begin{CD} X @>{f}>> Y\\ @VVV @VVV \\ \lambda(X) @>{\lambda(f)}>> \lambda(Y) \end{CD} $$ is commutative, where the vertical arrows are the said quasi-isomorphisms.