= Commutative-monoid enrichment
= Semi-additive structure
{synonym}
A commutative-monoid enrichment gives each hom-set a <commutative monoid> structure, with zero and addition, so that composition distributes over addition in both variables and annihilates zero. This is called a semi-additive structure in some conventions, including Cambridge Part III paper 119 of 2017. Other conventions reserve <semi-additive category> for categories with this enrichment and finite <biproducts>. A one-object category arising from a <semiring> has the enrichment without generally having those finite products.
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