Definition 12.6.2. Let $\mathcal{A}$ be an abelian category. Let $A, B \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{A})$. The set of isomorphism classes of extensions of $B$ by $A$ is denoted

\[ \mathop{\mathrm{Ext}}\nolimits _\mathcal {A}(B, A). \]

This is called the *$\mathop{\mathrm{Ext}}\nolimits $-group*.

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