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Theorems · Theorem · category theory

CategoryTheory.Limits.zero_of_to_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 : X ⟶ 0), f = 0

An arrow ending in the zero object is zero

Defined in
Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms
Cited by
1 results in Mathlib
Foundations
Depth 12 from the axioms · uses Classical.choice
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroMorphisms
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Functor.preservesZeroMorphisms_of_map_zero_object · cited by 1Functor.preservesZeroMorp…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.to_zero_ext · cited by 5HasZeroObject.to_zero_extLimits.zero_of_to_zeroCITED BYCITES

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Cited by1

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