= Short exact sequence in an abelian category
{title2=$0\to A\to B\to C\to0$}
= Short exact sequences in an abelian category
{synonym}
A short <exact sequence in an abelian category> is a sequence of the form $0\to A\xrightarrow{i}B\xrightarrow{p}C\to0$. Equivalently, $i$ is the <kernel in a category> of the <epimorphism> $p$. It splits if $p$ has a section; in that case the <additive category> splitting argument identifies $B$ with the <biproduct> $A\oplus C$. Categories of <modules> give familiar examples.
Back to article page
