Lemma is_functor_hom_functor_type : is_functor hom_functor_data. Proof. use make_dirprod. - intro; cbn. apply funextsec; intro. refine (id_right _ @ _). apply id_left. - intros ? ? ? ? ?. apply funextsec; intro; cbn. abstract (do 3 rewrite assoc; reflexivity). Defined.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.UnivalenceAxiom. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.PrecategoryBinProduct.