Theorems · Theorem · category theory

CategoryTheory.Limits.preservesInitial_of_iso

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (G : CategoryTheory.Functor C D) [inst_2 : CategoryTheory.Limits.HasInitial C]
  [inst_3 : CategoryTheory.Limits.HasInitial D] (f : ⊥_ D ≅ G.obj (⊥_ C)),
  CategoryTheory.Limits.PreservesColimit (CategoryTheory.Functor.empty C) G

If there is any isomorphism ⊥ ≅ G.obj ⊥, then G preserves initial objects.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasInitialCategoryTheory.Limits.HasInitial