proposition: Lemma constant_functor_composition_nat_z_iso (A B C : category) (b : B) (F : functor B C) : nat_z_iso (functor_composite (constant_functor A B b) F) (constant_functor A C (F b)).
proof: Proof. exists (constant_functor_composition_nat_trans A B C b F). intro; apply identity_is_z_iso. Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Chains.All