Definition cat_pseudmonic_is_pseudomonic_1cell {C₁ C₂ : bicat_of_univ_cats} {F : C₁ --> C₂} (HF : pseudomonic F) : pseudomonic_1cell F. Proof. use make_pseudomonic. - apply cat_faithful_is_faithful_1cell. exact (pr1 HF). - intros C₀ G₁ G₂ n Hn. refine (cat_pseudmonic_is_pseudomonic_1cell_inv HF n Hn ,, _ ,, _). + exact (is_invertible_cat_pseudmonic_is_pseudomonic_1cell_inv HF n Hn). + exact (cat_pseudmonic_is_pseudomonic_1cell_inv_eq HF n Hn). 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.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.UnivalenceOp. Require Import UniMath.Bicategories.Core.Examples.OpMorBicat. 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. Require Import UniMath.Bicategories.Morphisms.Examples.MorphismsInOp1Bicat.