End adj_eqs.
Section adj_eqs1.
Variables (C D : Category) (F : Functor D C) (G : Functor C D) (ad : Adj F G).
Variables (d d' : D) (c c' : C) (h : d' --> d) (k : c --> c')
(f : F d --> c) (g : d --> G c).

(* Specifications: *)
Lemma Adj_eq3 : ApAphi ad (f o k) =_S ApAphi ad f o FMor G k.
Lemma Adj_eq4 : ApAphi ad (FMor F h o f) =_S h o ApAphi ad f.
Lemma Adj_eq5 : ApAphi_inv ad (g o FMor G k) =_S ApAphi_inv ad g o k.
Lemma Adj_eq6 : ApAphi_inv ad (h o g) =_S FMor F h o ApAphi_inv ad g.
End adj_eqs1.