Definition conservative_1cell_to_conservative {B : bicat} {a b : B} {f : a --> b} (Hf : conservative_1cell f) (x : B) : conservative (post_comp x f). Proof. intros g₁ g₂ α Hα. apply is_inv2cell_to_is_z_iso. apply Hf. exact (z_iso_to_inv2cell (make_z_iso' _ 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.