2-ring

In mathematics, a categorical ring is, roughly, a category equipped with addition and multiplication. In other words, a categorical ring is obtained by replacing the underlying set of a ring by a category. For example, given a ring "R", let "C" be a category whose objects are the elements of the set "R" and whose morphisms are only the identity morphisms. Then "C" is a categorical ring. But the point is that one can also consider the situation in which an element of "R" comes with a "nontrivial automorphism" (cf. Lurie).
This line of generalization of a ring eventually leads to the notion of an "E""n"-ring.