Definition enriched_eso_ff_adjoint_equivalence {C₁ C₂ : enriched_cat V} (F : enriched_functor C₁ C₂) (HF₁ : essentially_surjective F) (HF₂ : fully_faithful_enriched_functor (enriched_functor_enrichment F)) : left_adjoint_equivalence F. Proof. use (orthogonal_left_right_to_adjequiv enriched_eso_ff_orthogonal_factorization_system). - exact HF₁. - exact HF₂. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Subcategory.Core. Require Import UniMath.CategoryTheory.Subcategory.Full. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.ImageEnriched. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.DisplayedBicats.Examples.EnrichedCats. Require Import UniMath.Bicategories.OrthogonalFactorization.Orthogonality. Require Import UniMath.Bicategories.OrthogonalFactorization.FactorizationSystem.