Theorems · Definition · category theory

CochainComplex.HomComplex.Cochain.leftShiftLinearEquiv

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      (R : Type u_1) →
        [inst_2 : Ring R] →
          [inst_3 : CategoryTheory.Linear R C] →
            (K L : CochainComplex C ℤ) →
              (n a n' : ℤ) →
                n + a = n' →
                  CochainComplex.HomComplex.Cochain K L n ≃ₗ[R]
                    CochainComplex.HomComplex.Cochain ((CategoryTheory.shiftFunctor (CochainComplex C ℤ) a).obj K) L n'

The additive equivalence Cochain K L n ≃+ Cochain (K⟦a⟧) L n' when n + a = n' and the category is R-linear.

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift

Cited by

3 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveRingCategoryTheory.Linear