Theorems · Definition · category theory

CategoryTheory.Functor.DenseAt

{C : Type u₁} →
  {D : Type u₂} →
    [inst : CategoryTheory.Category.{v₁, u₁} C] →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] → CategoryTheory.Functor C D → D → Type (max u₁ u₂ v₂)

A functor F : C ⥤ D is dense at Y : D if the obvious natural transformation F ⟶ F ⋙ 𝟭 D makes 𝟭 D a pointwise left Kan extension of F along itself at Y, i.e. Y identifies to the colimit of the obvious functor CostructuredArrow F Y ⥤ D.

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.DenseAt

Cited by

5 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category