proposition: Lemma isCoequalizer_path {hs : has_homsets C} {x y z : C} {f g : x --> y} {e : y --> z} {H H' : f · e = g · e} (iC : isCoequalizer f g e H) : isCoequalizer f g e H'.
proof: Proof. use make_isCoequalizer. intros w0 h H'0. use unique_exists. - exact (pr1 (pr1 (iC w0 h H'0))). - exact (pr2 (pr1 (iC w0 h H'0))). - intros y0. apply hs. - intros y0 X. exact (base_paths _ _ (pr2 (iC w0 h H'0) (tpair _ y0 X))). Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Retracts