Theorems · Definition · category theory

CategoryTheory.Functor.DenseAt.ofNatIso

{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 → {G : CategoryTheory.Functor C D} → (F ≅ G) → G.DenseAt Y

If F : C ⥤ D is dense at Y : D, and G is a functor that is isomorphic to F, then G is also dense at Y.

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.DenseAt

Cited by

1 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category