Theorems · Definition · category theory

CategoryTheory.Functor.IsDense.leftKanExtensionIso

{C : Type u₁} →
  {D : Type u₂} →
    [inst : CategoryTheory.Category.{v₁, u₁} C] →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (F : CategoryTheory.Functor C D) → [inst_2 : F.IsDense] → F.leftKanExtension F ≅ CategoryTheory.Functor.id D

If F is dense, the left Kan extension of F along F is isomorphic to the identity.

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Dense

Cited by

4 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsDense