Theorems · Definition · category theory

CategoryTheory.Functor.mapZeroObject

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        [inst_2 : CategoryTheory.Limits.HasZeroObject C] →
          [inst_3 : CategoryTheory.Limits.HasZeroObject D] →
            [inst_4 : CategoryTheory.Limits.HasZeroMorphisms C] →
              [inst_5 : CategoryTheory.Limits.HasZeroMorphisms D] →
                (F : CategoryTheory.Functor C D) → [F.PreservesZeroMorphisms] → F.obj 0 ≅ 0

A functor that preserves zero morphisms also preserves the zero object.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero

Cited by

9 results in Mathlib

Foundations

Depth 14 from the axioms · uses Classical.choice

Assumes

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