Theorems · Theorem · category theory

CategoryTheory.Functor.isRightKanExtension_iff_precomp

∀ {C : Type u_1} {C' : Type u_2} {H : Type u_3} {D : Type u_4} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} C'] [inst_2 : CategoryTheory.Category.{v_3, u_3} H]
  [inst_3 : CategoryTheory.Category.{v_4, u_4} D] {L : CategoryTheory.Functor C D} {F : CategoryTheory.Functor C H}
  (F' : CategoryTheory.Functor D H) (G : CategoryTheory.Functor C' C) [G.IsEquivalence] (α : L.comp F' ⟶ F),
  F'.IsRightKanExtension α ↔
    F'.IsRightKanExtension (CategoryTheory.CategoryStruct.comp (G.associator L F').hom (G.whiskerLeft α))

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Basic

Cited by

0 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsEquivalence