proposition: Proposition preserves_pullback_from_binproduct_equalizer_map_eq : BinProductArrow D Fxy h k · #F fp = BinProductArrow D Fxy h k · #F gp.
proof: Proof. unfold fp, gp. rewrite !functor_comp. rewrite !assoc. etrans. { apply maponpaths_2. apply (BinProductPr1Commutes _ _ _ Fxy). } refine (r @ _). refine (!_). apply maponpaths_2. apply (BinProductPr2Commutes _ _ _ Fxy). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.PullbackConstructions UniMath.CategoryTheory.Limits.Preservation UniMath.CategoryTheory.Limits.EquivalencePreservation UniMath.CategoryTheory.Limits.LimitIso UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.CompositesAndInverses UniMath.CategoryTheory.whiskering