Theorems · Inductive type · category theory

CategoryTheory.Functor.IsHomological

{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] →
          CategoryTheory.Functor C A →
            [inst_3 : CategoryTheory.Limits.HasZeroObject C] →
              [inst_4 : CategoryTheory.Preadditive C] →
                [inst_5 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] →
                  [CategoryTheory.Pretriangulated C] → [CategoryTheory.Abelian A] → Prop

A functor from a pretriangulated category to an abelian category is a homological functor if it sends distinguished triangles to exact sequences.

Defined in

Mathlib.CategoryTheory.Triangulated.HomologicalFunctor

Cited by

21 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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