Mathlib Map

Theorems · Theorem · category theory

CochainComplex.isStrictlyLE_shift

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  (K : CochainComplex C ℤ) (n : ℤ) [K.IsStrictlyLE n] (a n' : ℤ),
  a + n' = n → ((CategoryTheory.shiftFunctor (CochainComplex C ℤ) a).obj K).IsStrictlyLE n'
Defined in
Mathlib.Algebra.Homology.Embedding.CochainComplex
Cited by
1 results in Mathlib
Foundations
Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.PreadditiveCochainComplex.IsStrictlyLE
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.hasExt_iff · cited by 1CategoryTheory.hasExt_iffCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveCategoryTheory.shiftFunctor · cited by 1553CategoryTheory.shiftFunct…ComplexShape.up · cited by 1123ComplexShape.upCochainComplex · cited by 1016CochainComplexCochainComplex.shiftFunctorObjXIso · cited by 40CochainComplex.shiftFunct…CategoryTheory.Limits.IsZero.of_iso · cited by 35IsZero.of_isoCochainComplex.IsStrictlyLE · cited by 20CochainComplex.IsStrictly…CochainComplex.isZero_of_isStrictlyLE · cited by 8CochainComplex.isZero_of_…CochainComplex.isStrictlyLE_iff · cited by 2CochainComplex.isStrictly…CochainComplex.isStrictlyLE_s…CITED BYCITES

Cites11

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

Cited by1

Results whose statement or proof uses this declaration.