Theorems · Theorem · category theory

CategoryTheory.Functor.map_distinguished_op_exact

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.HasShift C ℤ]
  [inst_2 : CategoryTheory.Limits.HasZeroObject C] [inst_3 : CategoryTheory.Preadditive C]
  [inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] [inst_5 : CategoryTheory.Pretriangulated C]
  {A : Type u_2} [inst_6 : CategoryTheory.Category.{v_2, u_2} A] [inst_7 : CategoryTheory.Abelian A]
  (F : CategoryTheory.Functor Cᵒᵖ A) [inst_8 : F.IsHomological] (T : CategoryTheory.Pretriangulated.Triangle C)
  (hT : T ∈ CategoryTheory.Pretriangulated.distinguishedTriangles),
  ((CategoryTheory.Pretriangulated.shortComplexOfDistTriangle T hT).op.map F).Exact

Defined in

Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated

Cited by

1 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasShiftCategoryTheory.Limits.HasZeroObjectCategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.PretriangulatedCategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.Functor.IsHomological