Theorems · Theorem · category theory

HomotopyCategory.shift_quotient_obj

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  (K : HomologicalComplex C (ComplexShape.up ℤ)) (n : ℤ),
  (CategoryTheory.shiftFunctor (HomotopyCategory C (ComplexShape.up ℤ)) n).obj
      ((HomotopyCategory.quotient C (ComplexShape.up ℤ)).obj K) =
    (HomotopyCategory.quotient C (ComplexShape.up ℤ)).obj
      ((CategoryTheory.shiftFunctor (HomologicalComplex C (ComplexShape.up ℤ)) n).obj K)

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.Shift

Cited by

0 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive