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Theorems · Theorem · category theory

CategoryTheory.HasInjectiveDimensionLT.mk

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : CategoryTheory.HasExt C] {X : C} {n : ℕ},
  (∀ (i : ℕ), n ≤ i → ∀ ⦃Y : C⦄ (e : CategoryTheory.Abelian.Ext Y X i), e = 0) →
    CategoryTheory.HasInjectiveDimensionLT X n
Defined in
Mathlib.CategoryTheory.Abelian.Injective.Dimension
Cited by
2 results in Mathlib
Foundations
Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasExt
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.hasInjectiveDimensionLT_iff · cited by 6CategoryTheory.hasInjecti…CategoryTheory.hasInjectiveDimensionLT_of_enoughProjectives · cited by 0CategoryTheory.hasInjecti…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryEquiv.symm · cited by 3681Equiv.symmCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianCategoryTheory.HasExt · cited by 218CategoryTheory.HasExtCategoryTheory.Abelian.Ext · cited by 191Abelian.ExtEquiv.subsingleton · cited by 24Equiv.subsingletonCategoryTheory.HasInjectiveDimensionLT · cited by 23CategoryTheory.HasInjecti…CategoryTheory.HasExt.standard · cited by 22HasExt.standardCategoryTheory.Abelian.Ext.chgUniv · cited by 5Ext.chgUnivHasInjectiveDimensionLT.mkCITED BYCITES

Cites9

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Cited by2

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