Definition is_symmetric_monoidal_functor {C D : category} {M : monoidal C} {N : monoidal D} (HM : symmetric M) (HN : symmetric N) {F : functor C D} (HF : fmonoidal_lax M N F) : UU := ∏ (x y : C), monoidal_braiding_data (symmetric_to_braiding HN) (F x) (F y) · fmonoidal_preservestensordata HF y x = fmonoidal_preservestensordata HF x y · #F(monoidal_braiding_data (symmetric_to_braiding HM) x y).
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.whiskering. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Import BifunctorNotations. Import MonoidalNotations.