Theorems · Theorem · category theory

CategoryTheory.Functor.preservesTerminalObject_of_preservesZeroMorphisms

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  [CategoryTheory.Limits.HasZeroObject C] [CategoryTheory.Limits.HasZeroObject D]
  [inst_4 : CategoryTheory.Limits.HasZeroMorphisms C] [inst_5 : CategoryTheory.Limits.HasZeroMorphisms D]
  (F : CategoryTheory.Functor C D) [F.PreservesZeroMorphisms],
  CategoryTheory.Limits.PreservesLimit (CategoryTheory.Functor.empty C) F

Preserving zero morphisms implies preserving terminal objects.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero

Cited by

1 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphisms