Editing Full and faithful functors (section)

==Examples==
* The [[forgetful functor]] ''U'' : '''Grp''' → '''Set''' maps [[group (mathematics)|groups]] to their underlying set, "forgetting" the group operation. ''U'' is faithful because two [[group homomorphism|group homomorphisms]] with the same domains and codomains are equal if they are given by the same functions on the underlying sets. This functor is not full as there are functions between the underlying sets of groups that are not group homomorphisms. A category with a faithful functor to '''Set''' is (by definition) a [[concrete category]]; in general, that forgetful functor is not full.
* The inclusion functor '''Ab''' → '''Grp''' is fully faithful, since '''Ab''' (the [[category of abelian groups]]) is by definition the [[full subcategory]] of '''Grp''' induced by the abelian groups.