Lemma curry_functor_data_is_functor: is_functor curry_functor_data. Proof. split. - intro d. apply (nat_trans_eq E). intro c. cbn. unfold nat_trans_from_functor_fix_snd_morphism_arg_data. etrans. { apply maponpaths. apply binprod_id. } apply functor_id. - intros d1 d2 d3 f g. apply (nat_trans_eq E). intro c. cbn. unfold nat_trans_from_functor_fix_snd_morphism_arg_data. etrans. 2: { apply functor_comp. } apply maponpaths. apply dirprodeq; cbn. + apply pathsinv0. apply id_left. + apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. 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.FunctorCategory. Require Import UniMath.CategoryTheory.opp_precat.