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