Theorems · Theorem · category theory

CochainComplex.HomComplex.Cocycle.equivHomShift_comp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  {K L : CochainComplex C ℤ} {n : ℤ} {K' : CochainComplex C ℤ} (g : K' ⟶ K)
  (f : K ⟶ (CategoryTheory.shiftFunctor (CochainComplex C ℤ) n).obj L),
  CochainComplex.HomComplex.Cocycle.equivHomShift (CategoryTheory.CategoryStruct.comp g f) =
    (CochainComplex.HomComplex.Cocycle.equivHomShift f).precomp g

Defined in: Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift
Cited by: 1 results in Mathlib
Foundations: Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive

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Cites37

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

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zero_addproof · cited by 2,366
CategoryTheory.shiftFunctorstatement and proof · cited by 1,553
ComplexShape.upstatement · cited by 1,123

Cited by1

Results whose statement or proof uses this declaration.

CochainComplex.HomComplex.Cocycle.equivHomShift_symm_precompproof · cited by 2