#
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