Inmathematics, acategorical ring is, roughly, acategory equipped with addition and multiplication. In other words, a categorical ring is obtained by replacing theunderlying set of aring by a category. For example, given a ringR, letC be a category whoseobjects are the elements of thesetR and whosemorphisms are only the identity morphisms. ThenC is a categorical ring. But the point is that one can also consider the situation in which an element ofR comes with a "nontrivialautomorphism".[1]
This line of generalization of a ring eventually leads to the notion of anEn-ring.
Laplaza, M. (1972). "Coherence for distributivity".Coherence in categories. Lecture Notes in Mathematics. Vol. 281. Springer-Verlag. pp. 29–65.ISBN9783540379584.
