Theorems · Definition · category theory

CategoryTheory.Abelian.LeftResolution.chainComplex

{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 →
            A →
              [ι.Full] →
                [ι.Faithful] →
                  [inst_4 : CategoryTheory.Limits.HasZeroMorphisms C] → [CategoryTheory.Abelian A] → ChainComplex C ℕ

Given ι : C ⥤ A, Λ : LeftResolution ι, X : A, this is a chain complex which is a (functorial) resolution of A that is obtained inductively by using the epimorphisms given by Λ.

Defined in

Mathlib.Algebra.Homology.LeftResolution.Basic

Cited by

11 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.FullCategoryTheory.Functor.FaithfulCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Abelian