Homotopy Type Theory
fully faithful

Idea

Definition

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

$$F_{a,b} : hom_A(a,b) \to hom_B(F a, F b)$$

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

See also

Category theory

functor

equivalence of precategories

References

HoTT Book

category: category theory