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  "body": "\n## Summary\n\nAn injective resolution of an object $X$ is an exact sequence $0 \\to X \\to I^0 \\to I^1 \\to \\cdots$ in which every $I^n$ is injective.\nIt is the dual of a [[projective resolution|HK2AA1YSQ2]].\nRight [[derived functors|NPMC3K6J2F]] of a left exact functor are computed by applying the functor to an injective resolution.\nExamples are Ext in the second variable and sheaf cohomology.\n\n## Explanations\n\n### L1 human\n\nAn injective object is a target into which maps always extend.\nTo resolve $X$, embed it into an injective object, then embed the cokernel into another injective object, and so on.\nThe chain of injective objects remembers $X$ while being easy to map into.\nFor the integers, $\\Z$ sits inside the rationals $\\Q$, and the quotient $\\Q/\\Z$ is again injective.\nSo $0 \\to \\Z \\to \\Q \\to \\Q/\\Z \\to 0$ is an injective resolution of $\\Z$.\n",
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