Definition change_of_base_enriched_nat_trans {A B : enriched_precat Mon_V} {G H : enriched_functor A B} (a : enriched_nat_trans G H) : enriched_nat_trans (change_of_base_enriched_functor G) (change_of_base_enriched_functor H). Proof. use make_enriched_nat_trans. - intro x. exact (mon_functor_unit F · #F (a x)). - abstract (intros x y; cbn; rewrite <- lax_monoidal_functor_on_postcompose_underlying_morphism; rewrite <- lax_monoidal_functor_on_precompose_underlying_morphism; rewrite <- !(functor_comp F); apply maponpaths; apply enriched_nat_trans_ax). Defined.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.Propositions. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.EnrichedCats.Enriched.Enriched. Import MonoidalNotations.