Definition full_sub_category_is_functor {C₁ C₂ : category} {P : hsubtype C₁} {Q : hsubtype C₂} {F : C₁ ⟶ C₂} (HF : ∏ (x : C₁), P x → Q (F x)) : is_functor (full_sub_category_functor_data HF).
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.