# Homotopy Type Theory weak equivalence of precategories

## 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

Category theory

equivalence of precategories

functor

fully faithful functor

## References

HoTT book

category: category theory

Last revised on October 11, 2018 at 06:31:32. See the history of this page for a list of all contributions to it.