Definition conservative_to_conservative_1cell {B : bicat} {a b : B} {f : a --> b} (Hf : ∏ (x : B), conservative (post_comp x f)) : conservative_1cell f. Proof. intros x g₁ g₂ α Hα. apply is_z_iso_to_is_inv2cell. apply Hf. apply is_inv2cell_to_is_z_iso. exact Hα. 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.Isos. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Morphisms.FullyFaithful.