Definition functor_comp_enrichment_fully_faithful {V : monoidal_cat} {C₁ C₂ C₃ : category} {F₁ : C₁ ⟶ C₂} {F₂ : C₂ ⟶ C₃} {E₁ : enrichment C₁ V} {E₂ : enrichment C₂ V} {E₃ : enrichment C₃ V} {FE₁ : functor_enrichment F₁ E₁ E₂} {FE₂ : functor_enrichment F₂ E₂ E₃} (HF₁ : fully_faithful_enriched_functor FE₁) (HF₂ : fully_faithful_enriched_functor FE₂) : fully_faithful_enriched_functor (functor_comp_enrichment FE₁ FE₂). Proof. intros x y ; cbn. use is_z_isomorphism_comp. - apply HF₁. - apply HF₂. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.Limits.Terminal. Import MonoidalNotations.