Theorems · Theorem · category theory

CategoryTheory.TwoSquare.hasPointwiseLeftKanExtensionAt_iff

∀ {C₁ : Type u₁} {C₂ : Type u₂} {C₃ : Type u₃} {C₄ : Type u₄} {D : Type u₅} [inst : CategoryTheory.Category.{v₁, u₁} C₁]
  [inst_1 : CategoryTheory.Category.{v₂, u₂} C₂] [inst_2 : CategoryTheory.Category.{v₃, u₃} C₃]
  [inst_3 : CategoryTheory.Category.{v₄, u₄} C₄] [inst_4 : CategoryTheory.Category.{v₅, u₅} D]
  {T : CategoryTheory.Functor C₁ C₂} {L : CategoryTheory.Functor C₁ C₃} {R : CategoryTheory.Functor C₂ C₄}
  {B : CategoryTheory.Functor C₃ C₄} (w : CategoryTheory.TwoSquare T L R B) (F : CategoryTheory.Functor C₂ D) (X₃ : C₃)
  [(w.costructuredArrowRightwards X₃).Final],
  L.HasPointwiseLeftKanExtensionAt (T.comp F) X₃ ↔ R.HasPointwiseLeftKanExtensionAt F (B.obj X₃)

Defined in

Mathlib.CategoryTheory.GuitartExact.KanExtension

Cited by

2 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.Final