Theorems · Definition · category theory

CategoryTheory.Functor.mapDerivedCategorySingleFunctor

{C₁ : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C₁] →
    [inst_1 : CategoryTheory.Abelian C₁] →
      [inst_2 : HasDerivedCategory C₁] →
        {C₂ : Type u₂} →
          [inst_3 : CategoryTheory.Category.{v₂, u₂} C₂] →
            [inst_4 : CategoryTheory.Abelian C₂] →
              [inst_5 : HasDerivedCategory C₂] →
                (F : CategoryTheory.Functor C₁ C₂) →
                  [inst_6 : F.Additive] →
                    [inst_7 : CategoryTheory.Limits.PreservesFiniteLimits F] →
                      [inst_8 : CategoryTheory.Limits.PreservesFiniteColimits F] →
                        (n : ℤ) →
                          (DerivedCategory.singleFunctor C₁ n).comp F.mapDerivedCategory ≅
                            F.comp (DerivedCategory.singleFunctor C₂ n)

DerivedCategory.singleFunctor commutes with F and F.mapDerivedCategory.

Defined in

Mathlib.Algebra.Homology.DerivedCategory.ExactFunctor

Cited by

13 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianHasDerivedCategoryCategoryTheory.CategoryCategoryTheory.AbelianHasDerivedCategoryCategoryTheory.Functor.AdditiveCategoryTheory.Limits.PreservesFiniteLimitsCategoryTheory.Limits.PreservesFiniteColimits