Homotopy Type Theory
fully faithful



A functor F:ABF : A \to B is faithful if for all a,b:Aa,b : A, the function

F a,b:hom A(a,b)hom B(Fa,Fb)F_{a,b} : hom_A(a,b) \to hom_B(F a, F b)

is injective?, and full if for all a,b:Aa,b : A this function is surjective?. If it is both then FF is fully faithful

See also

Category theory functor equivalence of precategories


HoTT Book

category: category theory