Theorems · Theorem · category theory

CategoryTheory.Functor.isLimitConeOfIsRightKanExtension_lift

∀ {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] {c : CategoryTheory.Limits.Cone F}
  (hc : CategoryTheory.Limits.IsLimit c) (s : CategoryTheory.Limits.Cone F'),
  (F'.isLimitConeOfIsRightKanExtension α hc).lift s =
    hc.lift { pt := s.1, π := CategoryTheory.CategoryStruct.comp (L.whiskerLeft s.π) α }

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Basic

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsRightKanExtension