# Homotopy Type Theory fully faithful

## 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

Category theory

functor

equivalence of precategories

## References

HoTT Book

category: category theory

Last revised on September 18, 2018 at 12:28:33. See the history of this page for a list of all contributions to it.