Definition is_homotopical_functor {C C' : homotopical_category} (F : functor C C') : UU := ∏ (x y : C) (f : category_with_weq_pr2 C x y), category_with_weq_pr2 C' _ _ (# F (pr1 f)).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos.