Definition dialgebra_disp_cat : disp_cat C₁. Proof. use disp_struct. - exact (λ x, F x --> G x). - exact (λ x y hx hy f, hx · #G f = #F f · hy). - intros. apply C₂. - abstract (intros x hx ; cbn; rewrite !functor_id; rewrite id_left, id_right; apply idpath). - abstract (intros x y z f g hx hy hz hf hg ; cbn in *; rewrite !functor_comp; rewrite !assoc; rewrite hf; rewrite !assoc'; rewrite hg; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.CompositesAndInverses. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Projection. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence.