Definition inserter_conservative {B : bicat} {b₁ b₂ : B} {f g : b₁ --> b₂} {i : B} (m : i --> b₁) (α : m · f ==> m · g) (H : has_inserter_ump (make_inserter_cone i m α)) : conservative_1cell m. Proof. intros x g₁ g₂ β Hβ. use make_is_invertible_2cell. - exact (inserter_conservative_inv m α H β Hβ). - exact (inserter_conservative_rinv m α H β Hβ). - exact (inserter_conservative_linv m α H β Hβ). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.CategoryTheory.Categories.Dialgebras. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.DiscreteMorphisms.