Functor is a mapping between categories. Depends the way functors map morphisms they could be either covariant or contravariant. Covariant functors map morphisms as it is, contravariant functors flip morphisms:
Functor mapping operators in Я are Yonedified:
We compose functors by treating one of them as an argument of another one:
Functors which map from and into the same category are called endo functors.