Contravariant functor

A contravariant functor from a category $$\mathsf{C}$$ to a category $$\mathsf{D}$$ is a functor $$\mathscr{F} : \mathsf{C}^\text{op} \to \mathscr{D}$$ from the opposite category $$\mathsf{C}^\text{op}$$ of $$\mathsf{C}$$ to $$\mathsf{D}$$.