Theorems · Theorem · category theory

CategoryTheory.hasExt_iff

∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : HasDerivedCategory C],
  CategoryTheory.HasExt C ↔
    ∀ (X Y : C) (n : ℤ),
      0 ≤ n →
        Small.{w, w'}
          ((DerivedCategory.singleFunctor C 0).obj X ⟶
            (CategoryTheory.shiftFunctor (DerivedCategory C) n).obj ((DerivedCategory.singleFunctor C 0).obj Y))

Defined in

Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianHasDerivedCategory