## 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 $A$. ## See also ## [[Category theory]] [[precategory]] [[yoneda lemma]] ## References ## [[HoTT book]] category: category theory