Theorems · Definition · category theory

HomologicalComplex.tensorUnitIso

(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] →
          {I : Type u_2} →
            [inst_4 : AddMonoid I] →
              (c : ComplexShape I) →
                [inst_5 : DecidableEq I] →
                  (CategoryTheory.GradedObject.single₀ I).obj (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) ≅
                    (HomologicalComplex.tensorUnit C c).X

As a graded object, the single complex (single C c 0).obj (𝟙_ C) identifies to the unit (GradedObject.single₀ I).obj (𝟙_ C) of the tensor product of graded objects.

Defined in

Mathlib.Algebra.Homology.Monoidal

Cited by

2 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObjectAddMonoidDecidableEq