# faithful functor in a sentence

- A full and
*faithful functor* is necessarily injective on objects up to isomorphism. - Some authors define an "'embedding "'to be a full and
*faithful functor*. - Some authors define an "'embedding "'to be a full and
*faithful functor* that is injective on objects ( strictly ). - In practice, however, the choice of
*faithful functor* is often clear and in this case we simply speak of the " concrete category " C " ". - There is a fully
*faithful functor* from the category of abelian groups to "'Rng "'sending an abelian group to the associated rng of square zero. - It's difficult to find
*faithful functor* in a sentence. - Forgetful functors are almost always Concrete categories have forgetful functors to the category of sets indeed they may be " defined " as those categories that admit a
*faithful functor* to that category. - The product over the set of all prime numbers of the restriction of these functors to the category of torsion groups, is a
*faithful functor* from the category of torsion groups to the product over all prime numbers of the categories of " p "-torsion groups. - I have also shown that if \ mathcal { E } is a class of idempotents containing all identity morphisms of \ mathcal { C }, then there is a full &
*faithful functor* I : \ mathcal { C } \ to \ mathcal { C } [ \ mathcal { E } ].