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Theorems · Theorem · category theory

CategoryTheory.Limits.zero_of_from_zero

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroObject C]
  [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] {X : C} (f : 0 ⟶ X), f = 0

An arrow starting at the zero object is zero

Defined in
Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms
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Foundations
Depth 12 from the axioms · uses Classical.choice
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroMorphisms
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CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObject · cited by 1298Limits.HasZeroObjectCategoryTheory.Limits.HasZeroObject.zero' · cited by 115HasZeroObject.zero'CategoryTheory.Limits.HasZeroObject.from_zero_ext · cited by 8HasZeroObject.from_zero_e…Limits.zero_of_from_zeroCITED BYCITES

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