Definition full_sub_category_functor_data {C₁ C₂ : category} {P : hsubtype C₁} {Q : hsubtype C₂} {F : C₁ ⟶ C₂} (HF : ∏ (x : C₁), P x → Q (F x)) : functor_data (full_sub_category C₁ P) (full_sub_category C₂ Q). Proof. use make_functor_data. - exact (λ x, F (pr1 x) ,, HF (pr1 x) (pr2 x)). - exact (λ x y f, #F (pr1 f) ,, tt). 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.