Definition conservative_1cell_weq_conservative {B : bicat} {a b : B} (f : a --> b) : conservative_1cell f ≃ ∏ (x : B), conservative (post_comp x f). Proof. use weqimplimpl. - exact conservative_1cell_to_conservative. - exact conservative_to_conservative_1cell. - exact (isaprop_conservative_1cell f). - use impred ; intro. apply isaprop_conservative. 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.