Theorems · Definition · category theory

HomologicalComplex.singleMapHomologicalComplex

{ι : Type u_1} →
  {W₁ : Type u_3} →
    {W₂ : Type u_4} →
      [inst : CategoryTheory.Category.{v_2, u_3} W₁] →
        [inst_1 : CategoryTheory.Category.{v_3, u_4} W₂] →
          [inst_2 : CategoryTheory.Limits.HasZeroMorphisms W₁] →
            [inst_3 : CategoryTheory.Limits.HasZeroMorphisms W₂] →
              [inst_4 : CategoryTheory.Limits.HasZeroObject W₁] →
                [inst_5 : CategoryTheory.Limits.HasZeroObject W₂] →
                  (F : CategoryTheory.Functor W₁ W₂) →
                    [inst_6 : F.PreservesZeroMorphisms] →
                      (c : ComplexShape ι) →
                        [inst_7 : DecidableEq ι] →
                          (j : ι) →
                            (HomologicalComplex.single W₁ c j).comp (F.mapHomologicalComplex c) ≅
                              F.comp (HomologicalComplex.single W₂ c j)

Turning an object into a complex supported at j then applying a functor is the same as applying the functor then forming the complex.

Defined in

Mathlib.Algebra.Homology.Additive

Cited by

10 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroObjectCategoryTheory.Functor.PreservesZeroMorphismsDecidableEq