Transporting existence of specific limits across equivalences #
For now, we only treat the case of initial and terminal objects, but other special shapes can be added in the future.
theorem CategoryTheory.hasInitial_of_equivalence {C : Type u₁} [Category.{v₁, u₁} C] {D : Type u₂} [Category.{v₂, u₂} D] (e : Functor D C) [e.IsEquivalence] [Limits.HasInitial C] :
theorem CategoryTheory.Equivalence.hasInitial_iff {C : Type u₁} [Category.{v₁, u₁} C] {D : Type u₂} [Category.{v₂, u₂} D] (e : C ≌ D) :
theorem CategoryTheory.hasTerminal_of_equivalence {C : Type u₁} [Category.{v₁, u₁} C] {D : Type u₂} [Category.{v₂, u₂} D] (e : Functor D C) [e.IsEquivalence] [Limits.HasTerminal C] :
theorem CategoryTheory.Equivalence.hasTerminal_iff {C : Type u₁} [Category.{v₁, u₁} C] {D : Type u₂} [Category.{v₂, u₂} D] (e : C ≌ D) :