Theorems · Theorem · category theory

CategoryTheory.Functor.isLeftKanExtension_iff_postcompose

∀ {C : Type u_1} {H : Type u_3} {D : Type u_4} {D' : Type u_5} [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]
  [inst_3 : CategoryTheory.Category.{v_5, u_5} D'] {L : CategoryTheory.Functor C D} {L' : CategoryTheory.Functor D D'}
  {F₀ : CategoryTheory.Functor C H} {F₁ : CategoryTheory.Functor D H} (α : F₀ ⟶ L.comp F₁) [F₁.IsLeftKanExtension α]
  {F₂ : CategoryTheory.Functor D' H} (L'' : CategoryTheory.Functor C D') (e : L.comp L' ≅ L'') (β : F₁ ⟶ L'.comp F₂)
  (γ : F₀ ⟶ L''.comp F₂),
  autoParam
      (CategoryTheory.CategoryStruct.comp α
          (CategoryTheory.CategoryStruct.comp (L.whiskerLeft β)
            (CategoryTheory.CategoryStruct.comp (L.associator L' F₂).inv
              (CategoryTheory.Functor.whiskerRight e.hom F₂))) =
        γ)
      CategoryTheory.Functor.isLeftKanExtension_iff_postcompose._auto_1 →
    (F₂.IsLeftKanExtension β ↔ F₂.IsLeftKanExtension γ)

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Basic

Cited by

0 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLeftKanExtension