Theorems · Definition · category theory

CategoryTheory.Functor.homEquivOfIsRightKanExtension

{C : Type u_1} →
  {H : Type u_3} →
    {D : Type u_4} →
      [inst : CategoryTheory.Category.{v_1, u_1} C] →
        [inst_1 : CategoryTheory.Category.{v_3, u_3} H] →
          [inst_2 : CategoryTheory.Category.{v_4, u_4} D] →
            (F' : CategoryTheory.Functor D H) →
              {L : CategoryTheory.Functor C D} →
                {F : CategoryTheory.Functor C H} →
                  (α : L.comp F' ⟶ F) →
                    [F'.IsRightKanExtension α] → (G : CategoryTheory.Functor D H) → (G ⟶ F') ≃ (L.comp G ⟶ F)

If (F', α) is a right Kan extension of F along L, then this is the induced bijection (G ⟶ F') ≃ (L ⋙ G ⟶ F) for all G.

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Basic

Cited by

4 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsRightKanExtension