Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.triangEnvelopeIter_succ

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroObject C]
  [inst_2 : CategoryTheory.HasShift C ℤ] [inst_3 : CategoryTheory.Preadditive C]
  [inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] [inst_5 : CategoryTheory.Pretriangulated C]
  (P : CategoryTheory.ObjectProperty C) (n : ℕ),
  P.triangEnvelopeIter (n + 1) =
    ((P.shiftClosure ℤ).binaryProductsClosure.retractClosure.extensionProduct (P.triangEnvelopeIter n)).retractClosure

Defined in

Mathlib.CategoryTheory.Triangulated.Generators

Cited by

0 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.HasShiftCategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.Pretriangulated