More generally, in any abelian group, or even any commutative monoid, the group operation is often called ‘addition’ and written as , and then the identity element is called zero and written as . As a consequence, in any ring, or more generally any rig, the two binary operations are called ‘multiplication’ and ‘addition’, and the identity for addition is called zero.
Categorifying this idea, in any 2-rig the additive identity may be called zero. This is especially true in the case of a distributive category, that is a category with (at least finitary) products and coproducts, the former distributing over the latter. In this case the initial object, which serves as the identity for coproducts, is often called zero:
All these ideas can be, and have been, categorified further.