Section fscat.
Variables (C : Category) (I : Type) (a : I -> C).
Definition FSC_mor_setoid (i j : I) := a i --> a j.
(* composition *)
Definition Comp_FSC (i j l : I) :
Map2 (FSC_mor_setoid i j) (FSC_mor_setoid j l) (FSC_mor_setoid i l) :=
Op_comp (a i) (a j) (a l).
(* Id *)
Definition Id_FSC (i : I) := Id (a i).

Lemma Idr_FSC : Idr_law Comp_FSC Id_FSC.