# Homotopy Type Theory opposite precategory

## Idea

The opposite precategory is the precategory obtained by reversing the directions of the arrows.

## Definition

For a precategory $A$, its opposite $A^{op}$ is a precategory with the same type of objects, with $hom_{A^{op}}(a,b)\equiv hom_A(b,a)$, and with identities and composition inherited from $A$.

Category theory

precategory

yoneda lemma

## References

HoTT book

category: category theory

Created on September 6, 2018 at 13:57:14. See the history of this page for a list of all contributions to it.