Definition binproductleft_psfunctor: psfunctor CAT CAT. Proof. use make_psfunctor. - exact binproductleft_map_data. - exact binproductleft_map_laws. - split; red; cbn. + intro A. use tpair. * use make_nat_trans. -- intro ab. apply identity. -- intros ab ab' fg. cbn. apply pathsdirprod; rewrite id_left; apply id_right. * split; apply (nat_trans_eq (homset_property (productwithfixedelement _))); intro ab; cbn; apply pathsdirprod; apply id_left. + intros A1 A2 A3 F G. use tpair. * use make_nat_trans. -- intro a1b. apply identity. -- intros a1b a1b' fg. cbn. apply pathsdirprod; rewrite id_left; apply id_right. * split; apply (nat_trans_eq (homset_property (productwithfixedelement _))); intro a1b; cbn; apply pathsdirprod; apply id_left. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.CategoryTheory.UnitorsAndAssociatorsForEndofunctors. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.Examples.BicatOfCats. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.PseudoFunctors.Biadjunction. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Composition. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Identity. Require Import UniMath.Bicategories.Modifications.Modification. Import Bicat.Notations.