Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.retractClosure_extensionProduct_retractClosure_retractClosure

∀ {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 Q : CategoryTheory.ObjectProperty C),
  (P.retractClosure.extensionProduct Q.retractClosure).retractClosure = (P.extensionProduct Q).retractClosure

[Stacks Tag 0FX2](https://stacks.math.columbia.edu/tag/0FX2) (second part)

Defined in

Mathlib.CategoryTheory.Triangulated.Subcategory

Cited by

4 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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