Theorems · Theorem · category theory
CategoryTheory.hasInjectiveDimensionLT_iff
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] (X : C) (n : ℕ)
[inst_2 : CategoryTheory.HasExt C],
CategoryTheory.HasInjectiveDimensionLT X n ↔
∀ (i : ℕ), n ≤ i → ∀ ⦃Y : C⦄ (e : CategoryTheory.Abelian.Ext Y X i), e = 0- Cited by
- 6 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- CategoryTheory.HasExtstatement and proof · cited by 218
- CategoryTheory.Abelian.Extstatement and proof · cited by 191
- CategoryTheory.HasInjectiveDimensionLTstatement and proof · cited by 23
- CategoryTheory.Abelian.Ext.eq_zero_of_hasInjectiveDimensionLTproof · cited by 7
- CategoryTheory.HasInjectiveDimensionLT.mkproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.Retract.hasInjectiveDimensionLTproof · cited by 2
- CategoryTheory.hasInjectiveDimensionLT_of_geproof · cited by 1
- CategoryTheory.Limits.IsZero.hasInjectiveDimensionLT_zeroproof · cited by 1
- CategoryTheory.ShortComplex.ShortExact.hasInjectiveDimensionLT_X₁proof · cited by 1
- CategoryTheory.ShortComplex.ShortExact.hasInjectiveDimensionLT_X₃proof · cited by 1
- CategoryTheory.ShortComplex.ShortExact.hasInjectiveDimensionLT_X₂proof · cited by 0