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Theorems · Definition · category theory

CochainComplex.IsStrictlyLE

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] → CochainComplex C ℤ → ℤ → Prop

The condition that a cochain complex K is strictly ≤ n.

Defined in
Mathlib.Algebra.Homology.Embedding.CochainComplex
Cited by
20 results in Mathlib
Foundations
Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms

Around this declaration

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

DerivedCategory.TStructure.t · cited by 13TStructure.tCochainComplex.isZero_of_isStrictlyLE · cited by 8CochainComplex.isZero_of_…DerivedCategory.right_fac_of_isStrictlyLE · cited by 3DerivedCategory.right_fac…CochainComplex.isStrictlyLE_iff · cited by 2CochainComplex.isStrictly…CochainComplex.isSplitEpi_to_singleFunctor_obj_of_projective · cited by 1CochainComplex.isSplitEpi…CochainComplex.isStrictlyLE_shift · cited by 1CochainComplex.isStrictly…DerivedCategory.isLE_iff · cited by 1DerivedCategory.isLE_iffCochainComplex.exists_iso_single · cited by 1CochainComplex.exists_iso…CategoryTheory.hasExt_iff · cited by 1CategoryTheory.hasExt_iffDerivedCategory.exists_iso_Q_obj_of_isGE_of_isLE · cited by 1DerivedCategory.exists_is…DerivedCategory.exists_iso_Q_obj_of_isLE · cited by 1DerivedCategory.exists_is…DerivedCategory.exists_iso_singleFunctor_obj_of_isGE_of_isLE · cited by 1DerivedCategory.exists_is…DerivedCategory.from_singleFunctor_obj_eq_zero_of_projective · cited by 1DerivedCategory.from_sing…DerivedCategory.right_fac_of_isStrictlyLE_of_isStrictlyGE · cited by 0DerivedCategory.right_fac…CochainComplex.isKProjective_of_projective · cited by 0CochainComplex.isKProject…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCochainComplex · cited by 1016CochainComplexComplexShape.embeddingUpIntLE · cited by 21ComplexShape.embeddingUpI…HomologicalComplex.IsStrictlySupported · cited by 11HomologicalComplex.IsStri…CochainComplex.IsStrictlyLECITED BYCITES

Cites5

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

Cited by21

Results whose statement or proof uses this declaration.