Homotopy Type Theory
opposite precategory

Idea

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

Definition

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

See also

Category theory precategory yoneda lemma

References

HoTT book

category: category theory