Definition projection_fmonoidal {C : category} {D : disp_cat C} {M : monoidal C} (DM : disp_monoidal D M) : fmonoidal TM(DM) M π^{D}. Proof. exists (projection_fmonoidal_lax DM). split. - apply strictlytensorpreserving_is_strong. exact (projection_preservestensor_strictly DM). - apply strictlyunitpreserving_is_strong. exact (projection_preservesunit_strictly DM). 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.NaturalTransformations. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Monoidal. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Import BifunctorNotations. Import MonoidalNotations. Import DisplayedBifunctorNotations. Import DisplayedMonoidalNotations.