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Theorems · Theorem · category theory

CategoryTheory.Limits.IsZero.hasInjectiveDimensionLT_zero

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] {X : C},
  CategoryTheory.Limits.IsZero X → CategoryTheory.HasInjectiveDimensionLT X 0
Defined in
Mathlib.CategoryTheory.Abelian.Injective.Dimension
Cited by
1 results in Mathlib
Foundations
Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Abelian
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Around this declaration

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CategoryTheory.hasInjectiveDimensionLT_zero_iff_isZero · cited by 1CategoryTheory.hasInjecti…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idadd_zero · cited by 2707add_zeroCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianCategoryTheory.Limits.IsZero · cited by 306Limits.IsZeroCategoryTheory.HasExt · cited by 218CategoryTheory.HasExtCategoryTheory.Abelian.Ext · cited by 191Abelian.ExtCategoryTheory.Abelian.Ext.mk₀ · cited by 94Ext.mk₀CategoryTheory.Abelian.Ext.comp · cited by 80Ext.compCategoryTheory.HasInjectiveDimensionLT · cited by 23CategoryTheory.HasInjecti…CategoryTheory.HasExt.standard · cited by 22HasExt.standardCategoryTheory.Limits.IsZero.eq_zero_of_tgt · cited by 8IsZero.eq_zero_of_tgtCategoryTheory.Abelian.Ext.mk₀_zero · cited by 7Ext.mk₀_zeroCategoryTheory.Abelian.Ext.comp_zero · cited by 7Ext.comp_zeroIsZero.hasInjectiveDimensionL…CITED BYCITES

Cites17

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