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  "body": "\n## Summary\n\nA delta functor, or $\\delta$-functor, is a sequence of additive functors $T^0, T^1, T^2, \\dots$ between abelian categories, together with connecting maps.\nThese turn each short exact sequence into a long exact sequence.\nIt is the axiomatic form of a cohomology theory.\nThe right [[derived functors|NPMC3K6J2F]] of a left exact functor form a universal $\\delta$-functor, and universality is how one recognizes derived functors without resolutions.\n\n## Explanations\n\n### L1 human\n\nMany cohomology theories share one feature: a short exact sequence gives a long exact sequence that runs through all degrees.\nA delta functor keeps only this feature, as a list of functors with connecting maps between degrees.\nIt is universal if it is determined by its degree $0$ part.\nFor example, $\\operatorname{Ext}^n(M, -)$ for $n \\ge 0$ is a universal delta functor, determined by $\\Hom(M, -)$.\n",
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