proposition: Proposition preserves_pullback_from_binproduct_equalizer_pr2 : preserves_pullback_from_binproduct_equalizer_map · #F (PullbackPr2 (PBC z x y f g)) = k.
proof: Proof. cbn. rewrite functor_comp. rewrite !assoc. etrans. { apply maponpaths_2. apply (EqualizerCommutes FE). } 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