Theorems · Definition · category theory

CategoryTheory.Triangulated.TStructure.spectralObject

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      [inst_2 : CategoryTheory.Limits.HasZeroObject C] →
        [inst_3 : CategoryTheory.HasShift C ℤ] →
          [inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] →
            [inst_5 : CategoryTheory.Pretriangulated C] →
              CategoryTheory.Triangulated.TStructure C →
                [CategoryTheory.IsTriangulated C] → C → CategoryTheory.Triangulated.SpectralObject C EInt

The spectral object attached to an object X : C in a category equipped with a t-structure. It consists of all truncations of X.

Defined in

Mathlib.CategoryTheory.Triangulated.TStructure.SpectralObject

Cited by

4 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObjectCategoryTheory.HasShiftCategoryTheory.Functor.AdditiveCategoryTheory.PretriangulatedCategoryTheory.IsTriangulated