Jonathan Castello wrote:
> It wouldn't surprise me if there was a categorical way to frame this composition of structures. Like, a ring would be a special kind of object in the product category over rings.

At least in some cases, there is! You may already know that the slogan "A monoidal preorder is a monoid object in the category of preorders" is a slick way of rolling up all the definitions into one categorical concept. In the same sense, a ring is just a "monoid object" in the category of abelian groups. I haven't looked ahead to see if the book covers "monoid objects," but I hope we will in this course.