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  "body": "\n## Summary\n\nA [[functor|28NQ0KRHD3]] $F \\colon \\mathcal{C} \\to \\mathcal{D}$ is essentially surjective when every object of $\\mathcal{D}$ is isomorphic to $F(A)$ for some object $A$ of $\\mathcal{C}$.\nIt is surjectivity on objects up to isomorphism, which is the right notion in category theory, where isomorphic objects are interchangeable.\nA [[fully faithful|GRG8WEBSH5]] and essentially surjective functor is an [[equivalence of categories|K7A04ZBD92]].\n\n## Explanations\n\n### L1 human\n\nA functor might not hit every object of its target, but it can still reach every object up to isomorphism.\nFor example, the vector spaces $\\R^n$ for $n = 0, 1, 2, \\dots$ are only a few of all finite-dimensional real vector spaces.\nYet each finite-dimensional real vector space is isomorphic to one of them.\nSo including the spaces $\\R^n$ into all finite-dimensional spaces is essentially surjective, though far from surjective on objects.\n",
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