contravariant functor

contravariant functor (plural contravariant functors)

1. (category theory) A functor which maps a morphism f:X → Y to a morphism F(f):F(Y) → F(X), such that if ${\displaystyle h=g\circ f}$, then ${\displaystyle F(h)=F(f)\circ F(g)}$.

   A contravariant functor ${\displaystyle F:{\mathcal {C}}\rightarrow {\mathcal {D}}}$ is the same as a covariant functor ${\displaystyle F:{\mathcal {C}}^{op}\rightarrow {\mathcal {D}}}$.