Definition skewmonoidal_data : UU := ∑ (V : category)(tensor : V ⊠ V ⟶ V) (I : V), φ₁ tensor I ⟹ functor_identity V × functor_identity V ⟹ φ₂ tensor I × (tensor × (functor_identity _))%F ∙ tensor ⟹ (precategory_binproduct_unassoc _ _ _) ∙ (functor_identity V × tensor)%F ∙ tensor .
Require Import UniMath.Foundations.PartD. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.ProductCategory. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.whiskering.