#
Homotopy Type Theory

weak equivalence of precategories

## Idea

## Definition

A functor $F: A \to B$ is **essentially surjective** if for all $b:B$, there merely exists an $a:A$ such that $F a \cong b$.

We say that $F$ is a **weak equivalence** if it is fully faithful and essentially surjective.

For categories there is no difference between weak equivalences and equivalences.

## Properties

## See also

Category theory equivalence of precategories functor fully faithful functor

## References

HoTT book