Theorems · Theorem · category theory

CategoryTheory.Abelian.isoModSerre_kernel_eq_isLocal_of_rightAdjoint

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.Abelian C]
  [inst_3 : CategoryTheory.Abelian D] {G : CategoryTheory.Functor D C}
  [inst_4 : CategoryTheory.Limits.PreservesFiniteLimits G] [inst_5 : CategoryTheory.Limits.PreservesFiniteColimits G]
  {F : CategoryTheory.Functor C D} (adj : G ⊣ F) [F.Full] [F.Faithful],
  G.kernel.isoModSerre = CategoryTheory.ObjectProperty.isLocal fun x => x ∈ Set.range F.obj

Defined in

Mathlib.CategoryTheory.Abelian.SerreClass.Bousfield

Cited by

0 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.AbelianCategoryTheory.Limits.PreservesFiniteLimitsCategoryTheory.Limits.PreservesFiniteColimitsCategoryTheory.Functor.FullCategoryTheory.Functor.Faithful