Definition 12.6.1. Let $\mathcal{A}$ be an abelian category. Let $A, B \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{A})$. An *extension $E$ of $B$ by $A$* is a short exact sequence

An *morphism of extensions* between two extensions $0 \to A \to E \to B \to 0$ and $0 \to A \to F \to B \to 0$ means a morphism $f : E \to F$ in $\mathcal{A}$ making the diagram

commutative. Thus, the extensions of $B$ by $A$ form a category.

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Comment #2376 by Fred Rohrer on

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