Definition monoidal_functor_to_psfunctor: psfunctor M_as_bicat N_as_bicat. Proof. use make_psfunctor. - exact (monoidal_functor_to_psfunctor_map_data). - exact (monoidal_functor_to_psfunctor_map_laws). - split ; red; cbn. + intros H0. unfold two_cells_from_monoidal. exists (strong_monoidal_functor_ϵ_inv smF). exact (pr2 (strong_monoidal_functor_ϵ_is_z_iso smF)). + intros H0 H1 H2 a b. unfold two_cells_from_monoidal. exists (strong_monoidal_functor_μ_inv smF (a,,b)). exact (pr2 (strong_monoidal_functor_μ_is_nat_z_iso smF (a,,b))). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorsTensored. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.Examples.BicategoryFromMonoidal. Require Import UniMath.Bicategories.MonoidalCategories.MonoidalFromBicategory. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Import Bicat.Notations.