Lemma 13.27.6. Let $\mathcal{A}$ be an abelian category. Let $A$, $B$ be objects of $\mathcal{A}$. Then $\mathop{\mathrm{Ext}}\nolimits ^1_\mathcal {A}(B, A)$ is the group $\mathop{\mathrm{Ext}}\nolimits _\mathcal {A}(B, A)$ constructed in Homology, Definition 12.6.2.

**Proof.**
This is the case $i = 1$ of Lemma 13.27.5.
$\square$

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