Theorems · Definition · category theory

CategoryTheory.Functor.LeftExtension.isPointwiseLeftKanExtensionEquivOfIso

{C : Type u_1} →
  {D : Type u_2} →
    {H : Type u_4} →
      [inst : CategoryTheory.Category.{v_1, u_1} C] →
        [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
          [inst_2 : CategoryTheory.Category.{v_4, u_4} H] →
            {L : CategoryTheory.Functor C D} →
              {F : CategoryTheory.Functor C H} →
                {E E' : L.LeftExtension F} → (E ≅ E') → E.IsPointwiseLeftKanExtension ≃ E'.IsPointwiseLeftKanExtension

If two left extensions E and E' are isomorphic, E is a pointwise left Kan extension iff E' is.

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Pointwise

Cited by

0 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category