Coeq f g -> Coeq (O_functor f) (O_functor g) := functor_coeq (to O B) (to O A) (fun y => (to_O_natural f y)^) (fun y => (to_O_natural g y)^). Global Instance isequiv_O_coeq_cmp : O_inverts . Proof. rapply O_inverts_functor_coeq. Defined.
Require Import HoTT.Basics HoTT.Types. Require Import Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback. Require Import Homotopy.IdentitySystems. Require Import Colimits.Pushout.