Theorems · Theorem · category theory

CategoryTheory.Functor.isLeftKanExtension_of_iso

∀ {C : Type u_1} {H : Type u_3} {D : Type u_4} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_3, u_3} H] [inst_2 : CategoryTheory.Category.{v_4, u_4} D]
  {F' F'' : CategoryTheory.Functor D H} (e : F' ≅ F'') {L : CategoryTheory.Functor C D} {F : CategoryTheory.Functor C H}
  (α : F ⟶ L.comp F') (α' : F ⟶ L.comp F''),
  CategoryTheory.CategoryStruct.comp α (L.whiskerLeft e.hom) = α' →
    ∀ [F'.IsLeftKanExtension α], F''.IsLeftKanExtension α'

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Basic

Cited by

3 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLeftKanExtension