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- Full_and_faithful_functors abstract "In category theory, a faithful functor (resp. a full functor) is a functor that is injective (resp. surjective) when restricted to each set of morphisms that have a given source and target.Explicitly, let C and D be (locally small) categories and let F : C → D be a functor from C to D. The functor F induces a functionfor every pair of objects X and Y in C. The functor F is said to befaithful if FX,Y is injectivefull if FX,Y is surjectivefully faithful if FX,Y is bijectivefor each X and Y in C.A faithful functor need not be injective on objects or morphisms. That is, two objects X and X′ may map to the same object in D (which is why the range of a full and faithful functor is not necessarily isomorphic to C), and two morphisms f : X → Y and f′ : X′ → Y′ (with different domains/codomains) may map to the same morphism in D. Likewise, a full functor need not be surjective on objects or morphisms. There may be objects in D not of the form FX for some X in C. Morphisms between such objects clearly cannot come from morphisms in C.A full and faithful functor is necessarily injective on objects up to isomorphism. That is, if F : C → D is a full and faithful functor and then .".
- Full_and_faithful_functors wikiPageID "876534".
- Full_and_faithful_functors wikiPageRevisionID "591378847".
- Full_and_faithful_functors hasPhotoCollection Full_and_faithful_functors.
- Full_and_faithful_functors subject Category:Functors.
- Full_and_faithful_functors comment "In category theory, a faithful functor (resp. a full functor) is a functor that is injective (resp. surjective) when restricted to each set of morphisms that have a given source and target.Explicitly, let C and D be (locally small) categories and let F : C → D be a functor from C to D. The functor F induces a functionfor every pair of objects X and Y in C.".
- Full_and_faithful_functors label "Full and faithful functors".
- Full_and_faithful_functors label "Funtor pleno".
- Full_and_faithful_functors label "Funtores plenos e fiéis".
- Full_and_faithful_functors label "Treuer Funktor".
- Full_and_faithful_functors label "Volledige en trouwe functors".
- Full_and_faithful_functors sameAs Treuer_Funktor.
- Full_and_faithful_functors sameAs Funtor_pleno.
- Full_and_faithful_functors sameAs 충실한_함자와_충만한_함자.
- Full_and_faithful_functors sameAs Volledige_en_trouwe_functors.
- Full_and_faithful_functors sameAs Funtores_plenos_e_fiéis.
- Full_and_faithful_functors sameAs m.03kwhf.
- Full_and_faithful_functors sameAs Q1064276.
- Full_and_faithful_functors sameAs Q1064276.
- Full_and_faithful_functors wasDerivedFrom Full_and_faithful_functors?oldid=591378847.
- Full_and_faithful_functors isPrimaryTopicOf Full_and_faithful_functors.