Theorems · Definition · category theory

HomologicalComplex.Monoidal.inducingFunctorData

(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.Limits.HasZeroObject C] →
          [inst_4 : (CategoryTheory.MonoidalCategory.curriedTensor C).Additive] →
            [inst_5 : ∀ (X₁ : C), ((CategoryTheory.MonoidalCategory.curriedTensor C).obj X₁).Additive] →
              {I : Type u_2} →
                [inst_6 : AddMonoid I] →
                  (c : ComplexShape I) →
                    [inst_7 : c.TensorSigns] →
                      [inst_8 : ∀ (X₁ X₂ : CategoryTheory.GradedObject I C), X₁.HasTensor X₂] →
                        [inst_9 :
                            ∀ (X₁ : C),
                              CategoryTheory.Limits.PreservesColimit (CategoryTheory.Functor.empty C)
                                ((CategoryTheory.MonoidalCategory.curriedTensor C).obj X₁)] →
                          [inst_10 :
                              ∀ (X₂ : C),
                                CategoryTheory.Limits.PreservesColimit (CategoryTheory.Functor.empty C)
                                  ((CategoryTheory.MonoidalCategory.curriedTensor C).flip.obj X₂)] →
                            [inst_11 :
                                ∀ (X₁ X₂ X₃ X₄ : CategoryTheory.GradedObject I C), X₁.HasTensor₄ObjExt X₂ X₃ X₄] →
                              [inst_12 :
                                  ∀ (X₁ X₂ X₃ : CategoryTheory.GradedObject I C), X₁.HasGoodTensor₁₂Tensor X₂ X₃] →
                                [inst_13 :
                                    ∀ (X₁ X₂ X₃ : CategoryTheory.GradedObject I C), X₁.HasGoodTensorTensor₂₃ X₂ X₃] →
                                  [inst_14 : DecidableEq I] →
                                    CategoryTheory.Monoidal.InducingFunctorData (HomologicalComplex.forget C c)

The structure which allows to construct the monoidal category structure on HomologicalComplex C c from the monoidal category structure on graded objects.

Defined in

Mathlib.Algebra.Homology.Monoidal

Cited by

0 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObjectCategoryTheory.Functor.AdditiveCategoryTheory.Functor.AdditiveAddMonoidComplexShape.TensorSignsCategoryTheory.GradedObject.HasTensorCategoryTheory.Limits.PreservesColimitCategoryTheory.Limits.PreservesColimitCategoryTheory.GradedObject.HasTensor₄ObjExtCategoryTheory.GradedObject.HasGoodTensor₁₂TensorCategoryTheory.GradedObject.HasGoodTensorTensor₂₃DecidableEq