Definition has_bincoprod_ump_1_op_cell (q : @bincoprod_cocone (op2_bicat B) b₁ b₂) : bincoprod_1cell op_cell_cocone q. Proof. pose (k₁ := bincoprod_cocone_inl q). pose (k₂ := bincoprod_cocone_inr q). use make_bincoprod_1cell. - exact (bincoprod_ump_1cell ump k₁ k₂). - apply weq_op2_invertible_2cell. exact (inv_of_invertible_2cell (bincoprod_ump_1cell_inl ump _ k₁ k₂)). - apply weq_op2_invertible_2cell. exact (inv_of_invertible_2cell (bincoprod_ump_1cell_inr ump _ k₁ k₂)). 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.Invertible_2cells. Require Import UniMath.Bicategories.Core.Examples.OpCellBicat. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.Examples.MorphismsInOp2Bicat. Require Import UniMath.Bicategories.Colimits.Initial. Require Import UniMath.Bicategories.Colimits.Coproducts. Require Import UniMath.Bicategories.Colimits.Extensive. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.CommaObjects. Require Import UniMath.Bicategories.Limits.Examples.OpCellBicatLimits.