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  "body": "\n## Summary\n\nA short exact sequence is an [[exact sequence|JB7ZBFBA9C]] $0 \\to A \\to B \\to C \\to 0$ whose first and last terms are zero.\nIt says that $A$ is a subobject of $B$ and that $C$ is the corresponding quotient $B/A$.\nShort exact sequences are the basic input of homological algebra: functors are tested on them, and each gives a long exact sequence of derived functors.\n\n## Explanations\n\n### L1 human\n\nA short exact sequence describes an object $B$ as built from a piece $A$ and what is left over, $C$.\nThe first map puts $A$ inside $B$ without collapsing anything.\nThe second map sends $B$ onto $C$ and kills exactly the copy of $A$.\nFor example, $0 \\to \\Z \\xrightarrow{2} \\Z \\to \\Z/2\\Z \\to 0$ shows the integers built from the even integers and the two classes \"even\" and \"odd\".\nThe middle object is not always the direct sum of the outer two, as this example shows.\n",
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