Lemma BinCoproductsType : BinCoproducts type_precat. Proof. intros X Y. use tpair. - exact (coprod X Y,, inl,, inr). - apply isBinCoproduct'_to_isBinCoproduct. intro Z; apply (weqfunfromcoprodtoprod X Y Z). Defined.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.PartD. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Categories.Type.Core.