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.