Theorems · Definition · category theory

CategoryTheory.Functor.essImageDistTriang

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        (L : CategoryTheory.Functor C D) →
          [inst_2 : CategoryTheory.HasShift C ℤ] →
            [inst_3 : CategoryTheory.Preadditive C] →
              [inst_4 : CategoryTheory.Limits.HasZeroObject C] →
                [inst_5 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] →
                  [CategoryTheory.Pretriangulated C] →
                    [inst_7 : CategoryTheory.HasShift D ℤ] →
                      [L.CommShift ℤ] → Set (CategoryTheory.Pretriangulated.Triangle D)

Given a functor C ⥤ D from a pretriangulated category, this is the set of triangles in D that are in the essential image of distinguished triangles of C.

Defined in

Mathlib.CategoryTheory.Localization.Triangulated

Cited by

7 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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