{A} {D : A -> Type} `{DHasEquivs A D} {a b : A} {f : a $<~> b} {a' : D a} {b' : D b} (f' : DCatEquiv f a' b') : DCatEquiv (f^-1$) b' a'. Proof. snrapply dcate_adjointify. - exact (' f'). - exact f'. - exact (dcate_issect' f'). - exact (dcate_isretr' f'). Defined.
Require Import Basics.Overture. Require Import Basics.Tactics. Require Import Basics.Equivalences. Require Import Types.Sigma. Require Import WildCat.Core. Require Import WildCat.Displayed. Require Import WildCat.Equiv.