Theorems · Theorem · category theory

CategoryTheory.Functor.IsHomological.exact

∀ {C : Type u_1} {A : Type u_3} {inst : CategoryTheory.Category.{v_1, u_1} C} {inst_1 : CategoryTheory.HasShift C ℤ}
  {inst_2 : CategoryTheory.Category.{v_3, u_3} A} {F : CategoryTheory.Functor C A}
  {inst_3 : CategoryTheory.Limits.HasZeroObject C} {inst_4 : CategoryTheory.Preadditive C}
  {inst_5 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive} {inst_6 : CategoryTheory.Pretriangulated C}
  {inst_7 : CategoryTheory.Abelian A} [self : F.IsHomological] (T : CategoryTheory.Pretriangulated.Triangle C)
  (hT : T ∈ CategoryTheory.Pretriangulated.distinguishedTriangles),
  ((CategoryTheory.Pretriangulated.shortComplexOfDistTriangle T hT).map F).Exact

Defined in

Mathlib.CategoryTheory.Triangulated.HomologicalFunctor

Cited by

1 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Functor.IsHomological