Theorems · Definition · category theory

HomologicalComplex.rightUnitor

{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] →
                      (K : HomologicalComplex C c) →
                        [inst_8 : DecidableEq I] →
                          [inst_9 :
                              ∀ (X₁ : C),
                                CategoryTheory.Limits.PreservesColimit (CategoryTheory.Functor.empty C)
                                  ((CategoryTheory.MonoidalCategory.curriedTensor C).obj X₁)] →
                            K.tensorObj (HomologicalComplex.tensorUnit C c) ≅ K

The right unitor for the tensor product of homological complexes.

Defined in

Mathlib.Algebra.Homology.Monoidal

Cited by

0 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObjectCategoryTheory.Functor.AdditiveCategoryTheory.Functor.AdditiveAddMonoidComplexShape.TensorSignsDecidableEqCategoryTheory.Limits.PreservesColimit