Translation of "representable functor" into German

(category theory) Given a category C , a covariant representable functor h ^A sends each object X in category C to C ( A , X ), the set of arrows from A to X , and sends each arrow f : X → Y to a function from C ( A , X ) to C ( A , Y ) which maps each element s of C ( A , X ) to an element f \circ s of C ( A , Y ). A contravariant representable functor h _A sends each object X in category C to set C ( X , A ) and each arrow f : X → Y to a function from C ( Y , A ) to C ( X , A ) which maps each element s of C ( Y , A ) to an element s\circ f of C ( X , A ). Note: h ^A : C → Sets and h _A : C ^op → Sets , because h _A reverses the direction of the morphisms, whereas h ^A does not. [..]