Theorems · Theorem · category theory

CategoryTheory.Functor.leftKanExtensionIsoFiberwiseColimit_inv_app

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] (L : CategoryTheory.Functor C D) {H : Type u_3}
  [inst_2 : CategoryTheory.Category.{v_3, u_3} H] (F : CategoryTheory.Functor C H)
  [inst_3 : L.HasPointwiseLeftKanExtension F] [inst_4 : L.HasLeftKanExtension F] (X : D),
  (L.leftKanExtensionIsoFiberwiseColimit F).inv.app X =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Limits.HasColimit.isoOfNatIso
          (CategoryTheory.Functor.isoWhiskerRight (CategoryTheory.CostructuredArrow.ιCompGrothendieckProj L X) F)).hom
      (L.leftKanExtensionObjIsoColimit F X).inv

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Adjunction

Cited by

0 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.HasPointwiseLeftKanExtensionCategoryTheory.Functor.HasLeftKanExtension