Theorems · Theorem · category theory

CategoryTheory.Functor.Final.colimit_cocone_comp_aux

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {F : CategoryTheory.Functor C D} [inst_2 : F.Final] {E : Type u₃} [inst_3 : CategoryTheory.Category.{v₃, u₃} E]
  {G : CategoryTheory.Functor D E} (s : CategoryTheory.Limits.Cocone (F.comp G)) (j : C),
  CategoryTheory.CategoryStruct.comp (G.map (CategoryTheory.Functor.Final.homToLift F (F.obj j)))
      (s.ι.app (CategoryTheory.Functor.Final.lift F (F.obj j))) =
    s.ι.app j

Defined in

Mathlib.CategoryTheory.Limits.Final

Cited by

0 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.FinalCategoryTheory.Category