Theorems · Definition · category theory

CategoryTheory.ObjectProperty.IsStrongTriangulatedGenerator

{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 → Prop

An object property P is called a strong triangulated generator, if every object can be reached from objects in P by shifts, binary products, retracts and at most n extensions, for some fixed n.

Defined in

Mathlib.CategoryTheory.Triangulated.Generators

Cited by

2 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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