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  "body": "\n## Summary\n\nA [[functor|28NQ0KRHD3]] is faithful when it is injective on each set of morphisms between two fixed objects.\nIt is full when it is surjective on each such set, and fully faithful when it is both.\nA faithful functor loses no information about morphisms, and a fully faithful one identifies the morphisms of its source with those between the images.\nForgetful functors such as groups to sets are faithful but not full.\nFully faithful functors are the embeddings of category theory, and the Yoneda embedding is the main example.\nTogether with [[essential surjectivity|6ERBSBVF14]] they characterize [[equivalences of categories|K7A04ZBD92]].\n\n## Explanations\n\n### L1 human\n\nLook at all the arrows between two objects, and at all the arrows between their images.\nA functor gives a map from the first collection to the second.\nIt is faithful if different arrows stay different, and full if every arrow between the images comes from some arrow.\nForgetting that a group is a group is faithful, since a homomorphism is determined by its underlying function.\nIt is not full, because most functions between two groups are not homomorphisms.\n",
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