Theorems · Theorem · category theory

CategoryTheory.Functor.liftOfIsRightKanExtension_fac_app_assoc

∀ {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' : CategoryTheory.Functor D H) {L : CategoryTheory.Functor C D} {F : CategoryTheory.Functor C H}
  (α : L.comp F' ⟶ F) [inst_3 : F'.IsRightKanExtension α] (G : CategoryTheory.Functor D H) (β : L.comp G ⟶ F) (X : C)
  {Z : H} (h : F.obj X ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((F'.liftOfIsRightKanExtension α G β).app (L.obj X))
      (CategoryTheory.CategoryStruct.comp (α.app X) h) =
    CategoryTheory.CategoryStruct.comp (β.app X) h

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Basic

Cited by

0 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsRightKanExtension