{A} `{HasEquivs A} {a b : A} (f : a $-> b) (g : b $-> a) (r : f $o g $== Id b) (s : g $o f $== Id a) : cate_fun (cate_adjointify f g r s)^-1$ $== g. Proof. apply cate_inverse_sect. exact ((cate_buildequiv_fun f $@R _) $@ r). Defined.
Require Import Basics.Utf8 Basics.Overture Basics.Tactics Basics.Equivalences. Require Import WildCat.Core. Require Import WildCat.Opposite.