Theorems · Definition · category theory

CategoryTheory.Functor.mapDerivedCategory

{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) →
                  [F.Additive] →
                    [CategoryTheory.Limits.PreservesFiniteLimits F] →
                      [CategoryTheory.Limits.PreservesFiniteColimits F] →
                        CategoryTheory.Functor (DerivedCategory C₁) (DerivedCategory C₂)

The functor DerivedCategory C₁ ⥤ DerivedCategory C₂ induced by an exact functor F : C₁ ⥤ C₂ between abelian categories.

Defined in

Mathlib.Algebra.Homology.DerivedCategory.ExactFunctor

Cited by

18 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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