Theorems · Definition · category theory

CategoryTheory.Bicategory.LeftLift.IsKan.adjunction

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

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

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