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".^[1]

This line of generalization of a ring eventually leads to the notion of an E_n-ring.

See also

• Categorification
• Higher-dimensional algebra

References

• Laplaza, M. (1972). "Coherence for distributivity". Coherence in categories. Lecture Notes in Mathematics. Vol. 281. Springer-Verlag. pp. 29–65. ISBN 9783540379584.

External links

• http://ncatlab.org/nlab/show/2-rig

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