A standard short exact sequence is a complex $$0\to A\to B\to C \to 0$$ Based on this concept we get a lot of new concept in homological algebras. For example left exactness, right exactness, derived functor, etc. And we get some applications in other areas e.g algebraic topology.
Now let'us consider an exact sequence with more than 3 terms. For example 4 object or more as follows:
$$0\to A\to B\to C\to D \to 0$$
Do we get some thing new with these new concept of short exact sequence? Can we find some non trivial applications in homological algebra or algebraic topology?
Note that in this setting some concepts as left or right exactness have the obvious modifications.