Theorems · Definition · category theory

CategoryTheory.GradedObject.Monoidal.associator

{I : Type u} →
  [inst : AddMonoid I] →
    {C : Type u_1} →
      [inst_1 : CategoryTheory.Category.{v_1, u_1} C] →
        [inst_2 : CategoryTheory.MonoidalCategory C] →
          (X₁ X₂ X₃ : CategoryTheory.GradedObject I C) →
            [inst_3 : X₁.HasTensor X₂] →
              [inst_4 : (CategoryTheory.GradedObject.Monoidal.tensorObj X₁ X₂).HasTensor X₃] →
                [inst_5 : X₂.HasTensor X₃] →
                  [inst_6 : X₁.HasTensor (CategoryTheory.GradedObject.Monoidal.tensorObj X₂ X₃)] →
                    [X₁.HasGoodTensor₁₂Tensor X₂ X₃] →
                      [X₁.HasGoodTensorTensor₂₃ X₂ X₃] →
                        CategoryTheory.GradedObject.Monoidal.tensorObj
                            (CategoryTheory.GradedObject.Monoidal.tensorObj X₁ X₂) X₃ ≅
                          CategoryTheory.GradedObject.Monoidal.tensorObj X₁
                            (CategoryTheory.GradedObject.Monoidal.tensorObj X₂ X₃)

The associator isomorphism for graded objects.

Defined in

Mathlib.CategoryTheory.GradedObject.Monoidal

Cited by

12 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddMonoidCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.GradedObject.HasTensorCategoryTheory.GradedObject.HasTensorCategoryTheory.GradedObject.HasTensorCategoryTheory.GradedObject.HasTensorCategoryTheory.GradedObject.HasGoodTensor₁₂TensorCategoryTheory.GradedObject.HasGoodTensorTensor₂₃