Theorems · Theorem · category theory

CochainComplex.isZero_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.isZero_of_isLE._auto_1 →
    ∀ [K.IsLE n] [inst_3 : HomologicalComplex.HasHomology K i],
      CategoryTheory.Limits.IsZero (HomologicalComplex.homology K i)

Defined in: Mathlib.Algebra.Homology.Embedding.CochainComplex
Cited by: 1 results in Mathlib
Foundations: Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CochainComplex.IsLE HomologicalComplex.HasHomology

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Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
ComplexShape.upstatement · cited by 1,123
CochainComplexstatement and proof · cited by 1,016
HomologicalComplex.HasHomologystatement and proof · cited by 342
CategoryTheory.Limits.IsZerostatement · cited by 306
HomologicalComplex.homologystatement · cited by 209
CochainComplex.IsLEstatement and proof · cited by 11
HomologicalComplex.ExactAt.isZero_homologyproof · cited by 7
CochainComplex.exactAt_of_isLEproof · cited by 4

Cited by1

Results whose statement or proof uses this declaration.

CochainComplex.isLE_shiftproof · cited by 0