End Adjunct_Compose_assoc.
Section Adjunct_Id_unit_left.
Context {B C: Category}
{F : B –≻ C} {G : C –≻ B} (adj : F ⊣ G).

Theorem Adjunct_Id_unit_left :
match (Functor_id_unit_left _ _ F) in _ = Y return Adjunct Y _ with
eq_refl =>
match (Functor_id_unit_right _ _ G) in _ = Y return Adjunct _ Y with
eq_refl =>
Adjunct_Compose adj (Adjunct_Id C)
end
end
= adj.