Definition cocartesian_weq_cocartesian_via_adj (HB : is_univalent_2_1 B) : cocartesian_ob b ≃ cocartesian_ob_via_adj b T prod. Proof. use weqdirprodf. - exact (cocartesian_initial_weq_cocartesian_initial_via_adj HB). - exact (cocartesian_coprod_weq_cocartesian_coprod_via_adj HB). 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.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Preservation. 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.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.UnivalenceOp. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Limits.Final. Require Import UniMath.Bicategories.Limits.Products. Section FromAdj. End FromAdj. Section FromAdj. End FromAdj.