Theorems · Theorem · category theory

CategoryTheory.Functor.isIso_lanAdjunction_homEquiv_symm_iff

∀ {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] (L : CategoryTheory.Functor C D) {H : Type u_3}
  [inst_2 : CategoryTheory.Category.{v_3, u_3} H] [inst_3 : ∀ (F : CategoryTheory.Functor C H), L.HasLeftKanExtension F]
  {F : CategoryTheory.Functor C H} {G : CategoryTheory.Functor D H} (α : F ⟶ L.comp G),
  CategoryTheory.IsIso (((L.lanAdjunction H).homEquiv F G).symm α) ↔ G.IsLeftKanExtension α

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Adjunction

Cited by

1 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.HasLeftKanExtension