Functor

Let and be categories.
A functor consists of mappings

Satisfying:

Covariant
Contravariant
Forgetful Functor
Free Group Functor
Power Set Functor
Dual Space Functor
Opposite Functor
Monoid Homomorphism
Order Preserving Map
Group Action

Faithfull
Full
Essentially Injective
Essentially Surjective