proposition: Lemma is_functor_base_change_functor {c c' : C} (g : C⟦c,c'⟧) : is_functor (base_change_functor_data g).
proof: Proof. split. - intros x; apply (eq_mor_slicecat C); simpl. apply pathsinv0, PullbackArrowUnique; rewrite id_left, ?id_right; apply idpath. - intros x y z f1 f2; apply (eq_mor_slicecat C); simpl. apply pathsinv0, PullbackArrowUnique. + rewrite <- assoc, !PullbackArrow_PullbackPr1; apply idpath. + rewrite <- assoc, PullbackArrow_PullbackPr2, !assoc, PullbackArrow_PullbackPr2; apply idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Univalence UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis