Theorems · Theorem · category theory

CategoryTheory.Functor.descOfIsLeftKanExtension.congr_simp

∀ {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 α_1 : F ⟶ L.comp F') (e_α : α = α_1) [inst_3 : F'.IsLeftKanExtension α] (G : CategoryTheory.Functor D H)
  (β β_1 : F ⟶ L.comp G), β = β_1 → F'.descOfIsLeftKanExtension α G β = F'.descOfIsLeftKanExtension α_1 G β_1

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Basic

Cited by

5 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLeftKanExtension