Theorems · Definition · category theory

CategoryTheory.Bicategory.LeftExtension.IsKan.adjunction

{B : Type u} →
  [inst : CategoryTheory.Bicategory B] →
    {a b : B} →
      {f : a ⟶ b} →
        {t : CategoryTheory.Bicategory.LeftExtension f (CategoryTheory.CategoryStruct.id a)} →
          t.IsKan → (t.whisker f).IsKan → CategoryTheory.Bicategory.Adjunction f t.extension

A left Kan extension t of the identity along f that commutes with f, in the sense that t.whisker f is a left Kan extension, is a right adjoint to f. The unit of this adjoint is given by the unit of the Kan extension.

Defined in

Mathlib.CategoryTheory.Bicategory.Kan.Adjunction

Cited by

1 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Bicategory