Theorems · Definition · category theory

CategoryTheory.Functor.DenseAt.precompEquivOfFinal

{C : Type u₁} →
  {D : Type u₂} →
    [inst : CategoryTheory.Category.{v₁, u₁} C] →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {F : CategoryTheory.Functor C D} →
          {Y : D} →
            {C' : Type u_1} →
              [inst_2 : CategoryTheory.Category.{v_1, u_1} C'] →
                (G : CategoryTheory.Functor C' C) →
                  [(CategoryTheory.CostructuredArrow.pre G F Y).Final] → (G.comp F).DenseAt Y ≃ F.DenseAt Y

If the canonical functor CostructuredArrow (G ≫ F) Y ⥤ CostructuredArrow F Y is final, then G ⋙ F is dense at Y if and only if F is dense at Y.

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.DenseAt

Cited by

1 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.Final