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  "body": "\n## Summary\n\nA final functor $F \\colon \\mathcal{C} \\to \\mathcal{D}$ is a [[functor|28NQ0KRHD3]] such that restricting a diagram on $\\mathcal{D}$ along $F$ does not change its [[colimit|BJS1CGTKQ5]].\nIt is the categorical form of a cofinal subset of a [[directed set|D9RY4667K6]], as in [[cofinality|BAWHE1W6MH]].\nFinal functors let one compute a colimit over a smaller or simpler index category.\nSome authors call them cofinal functors; the dual notion is an initial functor.\n\n## Explanations\n\n### L1 human\n\nTo find the limit of a sequence, you may look only at its terms with even index, since they go just as far out.\nA final functor is the same idea for colimits in a category.\nFor example, if the index category has a terminal object, the colimit of any diagram is simply its value at that object.\nThis is because the functor that picks out the terminal object is final.\n",
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