Definition equifiers_in_slice_bicat {B : bicat} (ins_B : has_equifiers B) (b : B) : has_equifiers (slice_bicat b). Proof. intros h₁ h₂ f₁ f₂ α β. pose (e := ins_B (pr1 h₁) (pr1 h₂) (pr1 f₁) (pr1 f₂) (pr1 α) (pr1 β)). simple refine (make_ob_slice (pr12 e · pr2 h₁) ,, make_1cell_slice _ _ ,, _ ,, _). - exact (pr12 e). - apply id2_invertible_2cell. - abstract (use eq_2cell_slice ; cbn ; exact (pr122 e)). - apply equifier_ump_in_slice. exact (pr222 e). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Slice. Require Import UniMath.Bicategories.Limits.Final. Require Import UniMath.Bicategories.Limits.Products. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.Inserters. Require Import UniMath.Bicategories.Limits.Equifiers.