Theorems · Theorem · category theory

CategoryTheory.Functor.IsHomological.of_iso

∀ {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] [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] {F₁ F₂ : CategoryTheory.Functor C A}
  [F₁.IsHomological] (e : F₁ ≅ F₂), F₂.IsHomological

Defined in

Mathlib.CategoryTheory.Triangulated.HomologicalFunctor

Cited by

1 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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