Theorems · Definition · category theory

CategoryTheory.ObjectProperty.extensionProduct

{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] →
            [CategoryTheory.Pretriangulated C] →
              CategoryTheory.ObjectProperty C → CategoryTheory.ObjectProperty C → CategoryTheory.ObjectProperty C

An object X satisfies extensionProduct P Q if there exists a distinguished triangle Y ⟶ X ⟶ Z ⟶ Y⟦1⟧ such that Y satisfies P and Z satisfies Q.

Defined in

Mathlib.CategoryTheory.Triangulated.Subcategory

Cited by

24 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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