Theorems · Theorem · category theory

CochainComplex.HomComplex.Cochain.rightUnshift_rightShift

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  {K L : CochainComplex C ℤ} {n : ℤ} (γ : CochainComplex.HomComplex.Cochain K L n) (a n' : ℤ) (hn' : n' + a = n),
  (γ.rightShift a n' hn').rightUnshift n hn' = γ

Defined in: Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift
Cited by: 2 results in Mathlib
Foundations: Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive

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Cites19

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.Functor.objproof · cited by 19,642
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.Iso.homproof · cited by 7,684
CategoryTheory.Iso.invproof · cited by 6,514
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.Preadditivestatement and proof · cited by 3,309
CategoryTheory.Category.comp_idproof · cited by 2,119
CategoryTheory.shiftFunctorproof · cited by 1,553
CochainComplexstatement and proof · cited by 1,016
CochainComplex.HomComplex.Cochainstatement and proof · cited by 341
CategoryTheory.Iso.inv_hom_idproof · cited by 308

Cited by2

Results whose statement or proof uses this declaration.

CochainComplex.HomComplex.Cochain.δ_rightUnshiftproof · cited by 2
CochainComplex.HomComplex.CohomologyClass.toHom_mk_eq_zero_iffproof · cited by 1