2-ring

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a categorical ring is, roughly, a <a href="/facts/Category_(mathematics)/7WzxUThf">category</a> equipped with addition and multiplication. In other words, a categorical ring is obtained by replacing the <a href="/facts/Underlying_set/TkuXca24">underlying set</a> of a <a href="/facts/Ring_(mathematics)/JnCUXz63">ring</a> by a category. For example, given a ring R, let C be a category whose <a href="/facts/Object_(category_theory)/7WzxUThf">objects</a> are the elements of the <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> R and whose <a href="/facts/Morphism/Kdpuyz3S">morphisms</a> 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 <a href="/facts/Automorphism/WnyxNFkQ">automorphism</a>".
This line of generalization of a ring eventually leads to the notion of an <a href="/facts/En_ring/C1BeC4BR">En-ring</a>.

2-ring open-in-new

2-ring