A functor from the category to the category is faithful if for each pair of objects , the function
between hom sets is injective.
More abstractly, we may say a functor is faithful if it is -surjective – or loosely speaking, ‘surjective on equations between given morphisms’.
See also faithful morphism for a generalization to an arbitrary 2-category.
(The simple proof is spelled out for instance at epimorphism.)
Revised on September 30, 2016 04:00:16
by Urs Schreiber