Theorems · Definition · category theory

CochainComplex.shiftFunctorObjXIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      (K : CochainComplex C ℤ) → (n i m : ℤ) → m = i + n → (((CochainComplex.shiftFunctor C n).obj K).X i ≅ K.X m)

The canonical isomorphism ((shiftFunctor C n).obj K).X i ≅ K.X m when m = i + n.

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.Shift

Cited by

40 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive