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For questions about the derived categories of various abelian categories and questions regarding the derived category construction itself.
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Checking exactness of a triangle on stalks
Suppose I have a triangle
$$A \to B \to C \to A[1]$$
in $D(Ab(X))$, the derived category of abelian sheaves on some topological space $X$. For each $x \in X$, there is an exact functor $D(Ab(X)) \to D …