Theorems · Theorem · category theory

CochainComplex.HomComplex.Cocycle.equivHomShift_apply

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  {K L : CochainComplex C ℤ} {n : ℤ} (a : K ⟶ (CategoryTheory.shiftFunctor (CochainComplex C ℤ) n).obj L),
  CochainComplex.HomComplex.Cocycle.equivHomShift a = (CochainComplex.HomComplex.Cocycle.ofHom a).rightUnshift n ⋯

Defined in: Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift
Cited by: 2 results in Mathlib
Foundations: Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive

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Cites13

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

DFunLike.coestatement and proof · cited by 62,936
CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.Preadditivestatement and proof · cited by 3,309
CategoryTheory.shiftFunctorstatement and proof · cited by 1,553
ComplexShape.upstatement · cited by 1,123
AddEquivstatement · cited by 1,087
CochainComplexstatement and proof · cited by 1,016
CochainComplex.HomComplex.Cocyclestatement · cited by 130
CochainComplex.HomComplex.Cocycle.ofHomstatement · cited by 23
CochainComplex.HomComplex.Cocycle.equivHomShiftstatement and proof · cited by 23

Cited by2

Results whose statement or proof uses this declaration.

CochainComplex.HomComplex.Cocycle.equivHomShift_compproof · cited by 1
CochainComplex.HomComplex.Cocycle.equivHomShift_comp_shiftproof · cited by 1