{A} {D : A -> Type} `{DHasEquivs A D} {a b : A} {f : a $<~> b} {a' : D a} {b' : D b} (f' : DCatEquiv f a' b') : DGpdHom (cate_isretr f) (dcate_fun f' $o' f'^-1$') (DId b'). Proof. refine (_ $@' ' f'). refine (dcate_fun f' $@L' _). apply dcate_buildequiv_fun. 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.