Theorems · Theorem · category theory

CategoryTheory.Functor.isRightKanExtension_iff_isIso

∀ {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} (φ : F'' ⟶ F') {L : CategoryTheory.Functor C D} {F : CategoryTheory.Functor C H}
  (α : L.comp F' ⟶ F) (α' : L.comp F'' ⟶ F),
  CategoryTheory.CategoryStruct.comp (L.whiskerLeft φ) α = α' →
    ∀ [F'.IsRightKanExtension α], F''.IsRightKanExtension α' ↔ CategoryTheory.IsIso φ

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Basic

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsRightKanExtension