In the Hartshorne book (Algebraic Geometry), page 114, we have the following proposition:
Proposition 5.7. Let $X$ be a scheme. The kernel, cokernel, and image of any
morphism of quasi-coherent sheaves are quasi-coherent. Any extension of
quasi-coherent sheaves is quasi-coherent. If $X$ is noetherian, the same is
true for coherent sheaves.
My question is: what is an "extension of quasi-coherent sheaves"?
Best Answer
If $0 \rightarrow A \rightarrow B \rightarrow C \rightarrow 0$ is a short exact sequence, B is called an extension of $A$ by $C$.