Theorems · Theorem · category theory

CategoryTheory.Functor.mem_homologicalKernel_iff

∀ {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 : F.ShiftSequence ℤ] (X : C),
  F.homologicalKernel X ↔ ∀ (n : ℤ), CategoryTheory.Limits.IsZero ((F.shift n).obj X)

Defined in

Mathlib.CategoryTheory.Triangulated.HomologicalFunctor

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.HasShiftCategoryTheory.CategoryCategoryTheory.Functor.ShiftSequence