[Koshkin]

Regardless of the "ladder" (or any other attempts to organize algebraic structures), what I find interesting (and somewhat unexpected) is that each particular structure exhibits so many features exclusive to it and such a rich behavior that is not found in any other structures - even closely related ones (like, for example, commutative vs. non-commutative rings) - that these attempts of organizing them and of some kind generalization seem to have not much value. It is only category theory that has managed to bring in something of a common viewpoint on many mathematical constructs (and not just those in algebra).