Theorems · Theorem · category theory

CategoryTheory.Functor.initial_of_comp_full_faithful

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {E : Type u₃} [inst_2 : CategoryTheory.Category.{v₃, u₃} E] (F : CategoryTheory.Functor C D)
  (G : CategoryTheory.Functor D E) [G.Full] [G.Faithful] [(F.comp G).Initial], F.Initial

The hypotheses also imply that G is initial, see initial_of_comp_full_faithful'.

Defined in

Mathlib.CategoryTheory.Limits.Final

Cited by

5 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.FullCategoryTheory.Functor.FaithfulCategoryTheory.Functor.Initial