# 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 En-ring. (Wikipedia).

Matrix Multiplication 2x2 Times 2x1 Example

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## Related pages

Mathematics | Set (mathematics) | Higher-dimensional algebra | Automorphism | Ring (mathematics) | Categorification | Category (mathematics) | Morphism