Theorems · Definition · category theory

CategoryTheory.Functor.DenseAt.precompOfFinal

{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} →
            F.DenseAt Y →
              {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

If F : C ⥤ D is dense at Y : D, then so is G ⋙ F if the canonical functor CostructuredArrow (G ≫ F) Y ⥤ CostructuredArrow F Y is final. This holds in particular if G is an equivalence.

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.DenseAt

Cited by

0 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.Final