{A B : Type} (f : A <~> B) : O A <~> O B := Build_Equiv _ _ (O_functor f) _.
Require Import HoTT.Basics HoTT.Types. Require Import Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback. Require Import Homotopy.IdentitySystems. Require Import Colimits.Pushout.