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Theorems · Theorem · category theory

CochainComplex.exactAt_of_isGE

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  (K : CochainComplex C ℤ) (n i : ℤ),
  autoParam (i < n) CochainComplex.exactAt_of_isGE._auto_1 → ∀ [K.IsGE n], HomologicalComplex.ExactAt K i
Defined in
Mathlib.Algebra.Homology.Embedding.CochainComplex
Cited by
5 results in Mathlib
Foundations
Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCochainComplex.IsGE
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Around this declaration

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

CochainComplex.isGE_iff · cited by 3CochainComplex.isGE_iffCochainComplex.Plus.modelCategoryQuillen.exists_quasiIso_injective · cited by 1modelCategoryQuillen.exis…CochainComplex.isZero_of_isGE · cited by 1CochainComplex.isZero_of_…DerivedCategory.isGE_iff · cited by 1DerivedCategory.isGE_iffCochainComplex.isGE_of_ge · cited by 0CochainComplex.isGE_of_geCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsComplexShape.up · cited by 1123ComplexShape.upCochainComplex · cited by 1016CochainComplexHomologicalComplex.ExactAt · cited by 44HomologicalComplex.ExactAtComplexShape.embeddingUpIntGE · cited by 20ComplexShape.embeddingUpI…CochainComplex.IsGE · cited by 13CochainComplex.IsGEHomologicalComplex.exactAt_of_isSupported · cited by 11HomologicalComplex.exactA…CochainComplex.exactAt_of_isGECITED BYCITES

Cites8

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Cited by5

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