Theorems · Theorem · category theory

CategoryTheory.Functor.hasPointwiseLeftDerivedFunctorAt_iff

∀ {C : Type u₁} {D : Type u₂} {H : Type u₃} [inst : CategoryTheory.Category.{v₁, u₁} C]
  [inst_1 : CategoryTheory.Category.{v₂, u₂} D] [inst_2 : CategoryTheory.Category.{v₃, u₃} H]
  (F : CategoryTheory.Functor C H) (L : CategoryTheory.Functor C D) (W : CategoryTheory.MorphismProperty C)
  [L.IsLocalization W] (X : C), F.HasPointwiseLeftDerivedFunctorAt W X ↔ L.HasPointwiseRightKanExtensionAt F (L.obj X)

Defined in

Mathlib.CategoryTheory.Functor.Derived.PointwiseLeftDerived

Cited by

4 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalization