In a pointed category, the zero morphism is the composite through its zero object. Composition on either side by any morphism remains zero. In a commutative-monoid enrichment on a pointed category, the additive zero must coincide with this zero morphism: morphisms to and from the zero object belong to singleton hom-sets.
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In mathematics, particularly in the context of category theory and algebra, a **zero morphism** (or **null morphism**) is a special type of morphism that generalizes the idea of a zero element in algebraic structures like groups or rings to more abstract settings.