## Tag `010J`

Chapter 12: Homological Algebra > Section 12.6: Extensions

Definition 12.6.1. Let $\mathcal{A}$ be an abelian category. Let $A, B \in \mathop{\rm Ob}\nolimits(\mathcal{A})$. An

extension $E$ of $B$ by $A$is a short exact sequence $$ 0 \to A \to E \to B \to 0. $$

The code snippet corresponding to this tag is a part of the file `homology.tex` and is located in lines 1033–1042 (see updates for more information).

```
\begin{definition}
\label{definition-extension}
Let $\mathcal{A}$ be an abelian category.
Let $A, B \in \Ob(\mathcal{A})$.
An {\it extension $E$ of $B$ by $A$} is a short
exact sequence
$$
0 \to A \to E \to B \to 0.
$$
\end{definition}
```

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