Theorems · Definition · category theory

CategoryTheory.Bicategory.Adjunction.isAbsoluteLeftKan

{B : Type u} →
  [inst : CategoryTheory.Bicategory B] →
    {a b : B} →
      {f : a ⟶ b} →
        {u : b ⟶ a} →
          (adj : CategoryTheory.Bicategory.Adjunction f u) →
            (CategoryTheory.Bicategory.LeftExtension.mk u adj.unit).IsAbsKan

For an adjunction f ⊣ u, u is an absolute left Kan extension of the identity along f. The unit of this Kan extension is given by the unit of the adjunction.

Defined in

Mathlib.CategoryTheory.Bicategory.Kan.Adjunction

Cited by

1 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Bicategory