Lemma BinProductsType : BinProducts type_precat. Proof. intros X Y. use tpair. - exact ((X × Y),, dirprod_pr1,, dirprod_pr2). - apply isBinProduct'_to_isBinProduct. intro; apply (weqfuntoprodtoprod _ X Y). 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.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Categories.Type.Core.