Theorems · Definition · category theory

CategoryTheory.ProjectiveResolution.extMk

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Abelian C] →
      [inst_2 : CategoryTheory.HasExt C] →
        {X Y : C} →
          (R : CategoryTheory.ProjectiveResolution X) →
            {n : ℕ} →
              (f : R.complex.X n ⟶ Y) →
                (m : ℕ) →
                  n + 1 = m →
                    CategoryTheory.CategoryStruct.comp (R.complex.d m n) f = 0 → CategoryTheory.Abelian.Ext X Y n

Given a projective resolution R of an object X of an abelian category, this is a constructor for elements in Ext X Y n which takes as an input a "cocycle" f : R.cocomplex.X n ⟶ Y.

Defined in

Mathlib.CategoryTheory.Abelian.Projective.Ext

Cited by

11 results in Mathlib

Foundations

Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasExt