Theorems · Theorem · category theory

CategoryTheory.Functor.isLeftDerivedFunctor_iff_isRightKanExtension

∀ {C : Type u_1} {D : Type u_2} {H : Type u_3} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_3, u_2} D] [inst_2 : CategoryTheory.Category.{v_5, u_3} H]
  (LF : CategoryTheory.Functor D H) {F : CategoryTheory.Functor C H} {L : CategoryTheory.Functor C D}
  (α : L.comp LF ⟶ F) (W : CategoryTheory.MorphismProperty C) [inst_3 : L.IsLocalization W],
  LF.IsLeftDerivedFunctor α W ↔ LF.IsRightKanExtension α

Defined in: Mathlib.CategoryTheory.Functor.Derived.LeftDerived
Cited by: 1 results in Mathlib
Foundations: Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Category CategoryTheory.Functor.IsLocalization

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.compstatement and proof · cited by 6,529
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
CategoryTheory.Functor.IsLocalizationstatement and proof · cited by 432
CategoryTheory.Functor.IsRightKanExtensionstatement and proof · cited by 46
CategoryTheory.Functor.IsLeftDerivedFunctorstatement and proof · cited by 33
CategoryTheory.Functor.IsLeftDerivedFunctor.isRightKanExtensionproof · cited by 6

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.Functor.isLeftDerivedFunctor_iff_isIso_leftDerivedLiftproof · cited by 0