Theorems · Definition · category theory

CategoryTheory.Functor.leftDerivedToHomotopyCategory

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {D : Type u_1} →
      [inst_1 : CategoryTheory.Category.{v_1, u_1} D] →
        [inst_2 : CategoryTheory.Abelian C] →
          [CategoryTheory.HasProjectiveResolutions C] →
            [inst_4 : CategoryTheory.Abelian D] →
              (F : CategoryTheory.Functor C D) →
                [F.Additive] → CategoryTheory.Functor C (HomotopyCategory D (ComplexShape.down ℕ))

When F : C ⥤ D is an additive functor, this is the functor C ⥤ HomotopyCategory D (ComplexShape.down ℕ) which sends X : C to F applied to a projective resolution of X.

Defined in

Mathlib.CategoryTheory.Abelian.LeftDerived

Cited by

12 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasProjectiveResolutionsCategoryTheory.AbelianCategoryTheory.Functor.Additive