Theorems · Definition · category theory

CategoryTheory.Abelian.LeftResolution.reduced

{A : Type u_1} →
  {C : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_2} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_1} A] →
        {ι : CategoryTheory.Functor C A} →
          CategoryTheory.Abelian.LeftResolution ι →
            [inst_2 : CategoryTheory.Preadditive C] →
              [inst_3 : CategoryTheory.Preadditive A] →
                [ι.Additive] →
                  [CategoryTheory.IsIdempotentComplete A] →
                    [CategoryTheory.IsIdempotentComplete C] → CategoryTheory.Abelian.LeftResolution ι

Given an additive functor ι : C ⥤ A between idempotent complete categories, any Λ : LeftResolution ι induces a term Λ.reduced : LeftResolution ι such that Λ.reduced.F preserves zero morphisms.

Defined in

Mathlib.Algebra.Homology.LeftResolution.Reduced

Cited by

0 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.IsIdempotentCompleteCategoryTheory.IsIdempotentComplete