Section horz_comp.
Variables (A B C : Category) (F G : Functor A B) (F' G' : Functor B C)
(T : NT F G) (T' : NT F' G').
Definition Ast (a : A) : (F o_F F') a --> (G o_F G') a :=
T' (F a) o FMor G' (T a).

Lemma Ast_eq :
forall a : A, FMor F' (T a) o T' (G a) =_S T' (F a) o FMor G' (T a).