{A B A' B'} (f : A -> A') (g : B -> B') `{IsConnMap O _ _ f} `{IsConnMap O _ _ g} : IsConnMap O (functor_sum f g). Proof. apply conn_map_from_extension_elim; intros. apply extension_functor_sum; rapply ooextendable_conn_map_inO. 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.