Editing Full and faithful functors (section)

==Generalization to (∞, 1)-categories==
The notion of a functor being 'full' or 'faithful' does not translate to the notion of a [[Quasi-category|(∞, 1)-category.]] In an (∞, 1)-category, the maps between any two objects are given by a space only up to homotopy. Since the notion of injection and surjection are not homotopy invariant notions (consider an interval embedding into the real numbers vs. an interval mapping to a point), we do not have the notion of a functor being "full" or "faithful." However, we can define a functor of quasi-categories to be ''fully faithful'' if for every ''X'' and ''Y'' in ''C,'' the map <math>F_{X,Y}</math> is a [[Weak equivalence (homotopy theory)|weak equivalence]].