Theorems · Theorem · category theory

CategoryTheory.Functor.hasPointwiseLeftKanExtensionAt_iff_of_equivalence

∀ {C : Type u_1} {D : Type u_2} {D' : Type u_3} {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_3, u_3} D']
  [inst_3 : CategoryTheory.Category.{v_4, u_4} H] (L : CategoryTheory.Functor C D) (L' : CategoryTheory.Functor C D')
  (F : CategoryTheory.Functor C H) (E : D ≌ D') (eL : L.comp E.functor ≅ L') (Y : D) (Y' : D')
  (e : E.functor.obj Y ≅ Y'), L.HasPointwiseLeftKanExtensionAt F Y ↔ L'.HasPointwiseLeftKanExtensionAt F Y'

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Pointwise

Cited by

1 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category