Definition monad_enrichment {V : monoidal_cat} {C : category} (E : enrichment C V) (M : Monad C) : UU := ∑ (EM : functor_enrichment M E E), nat_trans_enrichment (η M) (functor_id_enrichment _) EM × nat_trans_enrichment (μ M) (functor_comp_enrichment EM EM) EM.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. Require Import UniMath.CategoryTheory.Monoidal.Categories.