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Theorems · Theorem · category theory

CategoryTheory.isZero_of_hasInjectiveDimensionLT_zero

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] (X : C)
  [CategoryTheory.HasInjectiveDimensionLT X 0], CategoryTheory.Limits.IsZero X
Defined in
Mathlib.CategoryTheory.Abelian.Injective.Dimension
Cited by
1 results in Mathlib
Foundations
Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasInjectiveDimensionLT
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Around this declaration

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

CategoryTheory.hasInjectiveDimensionLT_zero_iff_isZero · cited by 1CategoryTheory.hasInjecti…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idEquiv.symm · cited by 3681Equiv.symmle_refl · cited by 2061le_reflCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianEquiv.injective · cited by 464Equiv.injectiveCategoryTheory.Limits.IsZero · cited by 306Limits.IsZeroCategoryTheory.HasExt · cited by 218CategoryTheory.HasExtCategoryTheory.Abelian.Ext.mk₀ · cited by 94Ext.mk₀CategoryTheory.Limits.IsZero.iff_id_eq_zero · cited by 40IsZero.iff_id_eq_zeroCategoryTheory.HasInjectiveDimensionLT · cited by 23CategoryTheory.HasInjecti…CategoryTheory.HasExt.standard · cited by 22HasExt.standardCategoryTheory.Abelian.Ext.homEquiv₀ · cited by 13Ext.homEquiv₀CategoryTheory.Abelian.Ext.mk₀_zero · cited by 7Ext.mk₀_zeroCategoryTheory.Abelian.Ext.eq_zero_of_hasInjectiveDimensionLT · cited by 7Ext.eq_zero_of_hasInjecti…CategoryTheory.isZero_of_hasI…CITED BYCITES

Cites16

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Cited by1

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