The characteristic of a ring is an important algebraic concept (and a specific number), but it refers to elements, so - in my understanding - it is evil (from the point of view of category theory). So the question arises:
How is the characteristic of a ring defined and calculated categorically?
Given the category of rings, how is the characteristic - as a number - of its objects calculated:
- from their in- and outgoing arrows?
- from special functors?
- from or to which other categories?
- or what ever?