proposition: Lemma constant_functor_composition_nat_trans (A B C : category) (b : B) (F : functor B C) : nat_trans (functor_composite (constant_functor A B b) F) (constant_functor A C (F b)).
proof: Proof. use make_nat_trans. + intro; apply identity. + abstract (intro; intros; apply maponpaths_2; exact (functor_id F b)). 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