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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}

    Comments (2)

    Comment #2376 by Fred Rohrer (site) on February 14, 2017 a 6:50 am UTC

    Typo: $C$ should be $B$.

    Comment #2432 by Johan (site) on February 17, 2017 a 3:05 pm UTC

    Thanks, fixed here.

    There are also 4 comments on Section 12.6: Homological Algebra.

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