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  "body": "\n## Summary\n\nA reflective subcategory is a [[full subcategory|V3BFGKBJF7]] whose inclusion functor has a left [[adjoint|TZHF6ZM92S]], called the reflector.\nThe reflector sends each object to its best approximation inside the subcategory.\nAbelianization, [[sheafification|2HYK3KBQNA]] and the [[Stone–Čech compactification|D9MWP5C85W]] are reflectors.\nReflective subcategories inherit limits from the ambient category, and colimits through the reflector.\n\n## Explanations\n\n### L1 human\n\nAbelian groups form a part of the world of all groups.\nEvery group $H$ has a best abelian approximation, the quotient $H/[H, H]$ by its commutator subgroup.\nEvery homomorphism from $H$ to an abelian group passes through this quotient in exactly one way.\nA reflective subcategory is a part of a category where every object has such a best approximation.\n",
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