Definition make_symmetric_monoidal_disp_cat_locally_prop (V : sym_monoidal_cat) (D : disp_cat V) (LP : locally_propositional D) (T : ∏ x y : V, D x → D y → D (x ⊗ y)) (Tmor : ∏ (x y1 y2 : V) (g : V⟦ y1, y2 ⟧) (xx : D x) (yy1 : D y1) (yy2 : D y2), yy1 -->[g] yy2 → T x y1 xx yy1 -->[ x ⊗^{V}_{l} g] T x y2 xx yy2) (B : ∏ (x y : V) (xx : D x) (yy : D y), T x y xx yy -->[sym_mon_braiding V x y] T y x yy xx) (II : D (monoidal_unit V)) (lu_lu : ∏ (x : V) (xx : D x), T (monoidal_unit V) x II xx -->[mon_lunitor x] xx) (lu_lu_inv : ∏ (x : V) (xx : D x), xx -->[mon_linvunitor x] T (monoidal_unit V) x II xx) (assass : ∏ (x y z : V) (xx : D x) (yy : D y) (zz : D z), (T _ _ (T _ _ xx yy) zz) -->[mon_lassociator x y z] T _ _ xx (T _ _ yy zz)) (assassinv : ∏ (x y z : V) (xx : D x) (yy : D y) (zz : D z), T _ _ xx (T _ _ yy zz) -->[mon_rassociator x y z] (T _ _ (T _ _ xx yy) zz)) : ∑ DM : disp_monoidal D V, disp_symmetric DM V. Proof. use make_symmetric_monoidal_disp_cat_locally_prop'. - exact T. - exact Tmor. - exact B. - intro ; intros ; apply LP. - intro ; intros ; apply LP. - intro ; intros ; apply LP. - intro ; intros ; apply LP. - exact II. - exact lu_lu. - exact lu_lu_inv. - exact assass. - exact assassinv. - exact LP. 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.Core.Isos. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Projection. 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.WhiskeredDisplayedBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Monoidal. Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Cartesian. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Import MonoidalNotations.