Lemma cartesian_monoidal_has_enough_comm_comonoids_mor_mult_diag {c1 c2 : V} (m1 : disp_cat_of_commutative_comonoids V c1) (m2 : disp_cat_of_commutative_comonoids V c2) (f : V ⟦ c1, c2 ⟧) : δ_{(_ ,, pr1 m1) : comonoid V} · f #⊗ f = f · δ_{(_ ,, pr1 m2) : comonoid V}. Proof. refine (_ @ cartesian_monoidal_has_enough_comonoids_mor_comult f @ _). -- apply maponpaths_2. apply comult_is_diag. -- apply maponpaths. apply pathsinv0, comult_is_diag. Qed.
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.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.catiso. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Projection. Require Import UniMath.CategoryTheory.DisplayedCats.CatIsoDisplayed. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Import BifunctorNotations. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Monoidal. Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal. Require Import UniMath.CategoryTheory.Monoidal.Structure.Cartesian. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.SymmetricDiagonal. Require Import UniMath.CategoryTheory.Monoidal.Comonoids.Category. Require Import UniMath.CategoryTheory.Monoidal.Comonoids.Tensor. Require Import UniMath.CategoryTheory.Monoidal.Comonoids.Monoidal. Require Import UniMath.CategoryTheory.Monoidal.Comonoids.Symmetric. Import MonoidalNotations. Import ComonoidNotations. End CartesianFromComonoidsToCartesian. *)