Definition:Functor/Contravariant/Definition 2

Definition
Let $\mathbf C$ and $\mathbf D$ be metacategories.

A contravariant functor $F : \mathbf C \to \mathbf D$ is a covariant functor:
 * $F: \mathbf C^{\text{op}} \to \mathbf D$

where $\mathbf C^{\text{op}}$ is the dual category of $\mathbf C$.

Also see

 * Equivalence of Definitions of Contravariant Functor