Let $\mathcal{C}$ and $\mathcal{D}$ be abelian categories.
An exact functor $F:\mathcal{C}\to\mathcal{D}$ preserves exactness of short exact sequences:
$$0\to A\to B\to C\to 0$$ goes to $$0\to F(A)\to F(B)\to F(C)\to 0$$
I don't believe that this implies long exact sequences are sent to long exact sequences.
0) Am I wrong? If not:
1) What tools do we have to measure the failure of $F$ in taking a long exact to a long exact?
2) Is there a name for a functor that takes long exact sequences to long exact sequences?