that at least covers some part of rings. On a theoretical level, all rings arise like that (i.e. as endomorphisms (= morphisms from an object to itself) in an category with addition on morphisms, but in practice, there seems another phenomenon which is more common for commutative rings. Suppose you have a set $X$ and a ring $R$ (say for example a field), then the set of all maps (of sets) from $X$ to $R$ is a ring with pointwise addition and multiplication.
It might be that you have some class of functions to a ring that is closed under addition and multiplication like continuous, different…