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Theorems · Theorem · category theory

CochainComplex.exactAt_of_isLE

∀ {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 (n < i) CochainComplex.exactAt_of_isLE._auto_1 → ∀ [K.IsLE n], HomologicalComplex.ExactAt K i
Defined in
Mathlib.Algebra.Homology.Embedding.CochainComplex
Cited by
4 results in Mathlib
Foundations
Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCochainComplex.IsLE
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Around this declaration

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

CochainComplex.isLE_iff · cited by 3CochainComplex.isLE_iffCochainComplex.isZero_of_isLE · cited by 1CochainComplex.isZero_of_…DerivedCategory.isLE_iff · cited by 1DerivedCategory.isLE_iffCochainComplex.isLE_of_le · cited by 0CochainComplex.isLE_of_leCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsComplexShape.up · cited by 1123ComplexShape.upCochainComplex · cited by 1016CochainComplexHomologicalComplex.ExactAt · cited by 44HomologicalComplex.ExactAtComplexShape.embeddingUpIntLE · cited by 21ComplexShape.embeddingUpI…HomologicalComplex.exactAt_of_isSupported · cited by 11HomologicalComplex.exactA…CochainComplex.IsLE · cited by 11CochainComplex.IsLECochainComplex.exactAt_of_isLECITED BYCITES

Cites8

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Cited by4

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