Definition one_types_inserter_ump_1 {X Y : one_types} (f g : X --> Y) : has_inserter_ump_1 (one_types_inserter_cone f g). Proof. intro q. use make_inserter_1cell. - exact (λ x, inserter_cone_pr1 q x ,, inserter_cone_cell q x). - use make_invertible_2cell. + exact (λ x, idpath _). + apply one_type_2cell_iso. - abstract (use funextsec ; intro x ; cbn ; unfold homotcomp, funhomotsec, homotfun ; cbn ; rewrite !pathscomp0rid ; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.OneTypes. 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.