Definition is_invertible_2cell_hcomp {C : bicat} {X Y Z : C} {f₁ g₁ : C⟦Y,Z⟧} {f₂ g₂ : C⟦X,Y⟧} (η₁ : f₁ ==> g₁) (η₂ : f₂ ==> g₂) (inv_η₁ : is_invertible_2cell η₁) (inv_η₂ : is_invertible_2cell η₂) : is_invertible_2cell (η₁ ⋆⋆ η₂). Proof. use make_is_invertible_2cell. - exact (inv_η₁^-1 ⋆⋆ inv_η₂^-1). - abstract (rewrite <- hcomp_vcomp, !vcomp_rinv; apply hcomp_identity). - abstract (rewrite <- hcomp_vcomp, !vcomp_linv; apply hcomp_identity). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations.