Definition full_sub_category_functor {C₁ C₂ : category} (P : hsubtype C₁) (Q : hsubtype C₂) (F : C₁ ⟶ C₂) (HF : ∏ (x : C₁), P x → Q (F x)) : full_sub_category C₁ P ⟶ full_sub_category C₂ Q. Proof. use make_functor. - exact (full_sub_category_functor_data HF). - exact (full_sub_category_is_functor HF). Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Subcategory.Core.