Theorems · Theorem · category theory

CategoryTheory.Functor.initial_comp_equivalence

∀ {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) [F.Initial] [G.IsEquivalence], (F.comp G).Initial

See also the strictly more general initial_comp below.

Defined in

Mathlib.CategoryTheory.Limits.Final

Cited by

1 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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