Theorems · Theorem · category theory

CategoryTheory.Functor.lanCompColimIso_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] [inst_3 : ∀ (F : CategoryTheory.Functor C H), L.HasLeftKanExtension F]
  [inst_4 : CategoryTheory.Limits.HasColimitsOfShape C H] [inst_5 : CategoryTheory.Limits.HasColimitsOfShape D H]
  (X : CategoryTheory.Functor C H),
  L.lanCompColimIso.inv.app X = ((L.lan.obj X).colimitIsoOfIsLeftKanExtension (L.lanUnit.app X)).inv

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Adjunction

Cited by

0 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.HasLeftKanExtensionCategoryTheory.Limits.HasColimitsOfShapeCategoryTheory.Limits.HasColimitsOfShape