A functor from the category to the category is faithful if for each pair of objects , the function
F : C(x,y) \to D(F(x), F(y))
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.
Revised on December 21, 2011 19:22:45
by Urs Schreiber