Theorems · Theorem · category theory

CategoryTheory.Functor.rightKanExtension_hom_ext

∀ {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]
  (L : CategoryTheory.Functor C D) (F : CategoryTheory.Functor C H) [inst_3 : L.HasRightKanExtension F]
  {G : CategoryTheory.Functor D H} (γ₁ γ₂ : G ⟶ L.rightKanExtension F),
  CategoryTheory.CategoryStruct.comp (L.whiskerLeft γ₁) (L.rightKanExtensionCounit F) =
      CategoryTheory.CategoryStruct.comp (L.whiskerLeft γ₂) (L.rightKanExtensionCounit F) →
    γ₁ = γ₂

Defined in: Mathlib.CategoryTheory.Functor.KanExtension.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Category CategoryTheory.Functor.HasRightKanExtension

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.compstatement · cited by 6,529
CategoryTheory.Functor.whiskerLeftstatement and proof · cited by 496
CategoryTheory.Functor.HasRightKanExtensionstatement and proof · cited by 38
CategoryTheory.Functor.rightKanExtensionCounitstatement and proof · cited by 11
CategoryTheory.Functor.rightKanExtensionstatement and proof · cited by 11
CategoryTheory.Functor.hom_ext_of_isRightKanExtensionproof · cited by 4

Cited by1

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CategoryTheory.Functor.rightKanExtension_hom_ext_iffproof · cited by 0