Theorems · Definition · category theory

HomologicalComplex.associator

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      [inst_2 : CategoryTheory.Preadditive C] →
        [inst_3 : (CategoryTheory.MonoidalCategory.curriedTensor C).Additive] →
          [inst_4 : ∀ (X₁ : C), ((CategoryTheory.MonoidalCategory.curriedTensor C).obj X₁).Additive] →
            {I : Type u_2} →
              [inst_5 : AddMonoid I] →
                {c : ComplexShape I} →
                  [inst_6 : c.TensorSigns] →
                    [inst_7 : DecidableEq I] →
                      (K₁ K₂ K₃ : HomologicalComplex C c) →
                        [inst_8 : K₁.HasTensor K₂] →
                          [inst_9 : K₂.HasTensor K₃] →
                            [inst_10 : (K₁.tensorObj K₂).HasTensor K₃] →
                              [inst_11 : K₁.HasTensor (K₂.tensorObj K₃)] →
                                [K₁.HasGoodTensor₁₂ K₂ K₃] →
                                  [K₁.HasGoodTensor₂₃ K₂ K₃] →
                                    (K₁.tensorObj K₂).tensorObj K₃ ≅ K₁.tensorObj (K₂.tensorObj K₃)

The associator isomorphism for the tensor product of homological complexes.

Defined in

Mathlib.Algebra.Homology.Monoidal

Cited by

0 results in Mathlib

Foundations

Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.Functor.AdditiveAddMonoidComplexShape.TensorSignsDecidableEqHomologicalComplex.HasTensorHomologicalComplex.HasTensorHomologicalComplex.HasTensorHomologicalComplex.HasTensorHomologicalComplex.HasGoodTensor₁₂HomologicalComplex.HasGoodTensor₂₃