Theorems · Definition · category theory

CategoryTheory.Abelian.Ext.homEquiv

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Abelian C] →
      [inst_2 : CategoryTheory.HasExt C] →
        {X Y : C} →
          [inst_3 : HasDerivedCategory C] →
            {n : ℕ} →
              CategoryTheory.Abelian.Ext X Y n ≃
                CategoryTheory.ShiftedHom ((DerivedCategory.singleFunctor C 0).obj X)
                  ((DerivedCategory.singleFunctor C 0).obj Y) ↑n

When an instance of [HasDerivedCategory.{w'} C] is available, this is the bijection between Ext.{w} X Y n and a type of morphisms in the derived category.

Defined in

Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic

Cited by

8 results in Mathlib

Foundations

Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasExtHasDerivedCategory