Theorems · Definition · category theory

CategoryTheory.Functor.lanUnit

{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] →
                CategoryTheory.Functor.id (CategoryTheory.Functor C H) ⟶
                  L.lan.comp ((CategoryTheory.Functor.whiskeringLeft C D H).obj L)

The natural transformation F ⟶ L ⋙ (L.lan).obj G.

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Adjunction

Cited by

16 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.HasLeftKanExtension