  This paper presents a simple generalization of the basic atomic read/write
register object, whose genericity parameter spans the whole set of integers and
is such that its k-parameterized instance has exactly consensus number k. This
object, whose definition is pretty natural, is a sliding window register of
size k. Its interest lies in its simplicity and its genericity dimension which
provides a global view capturing the whole consensus hierarchy. Hence, this
short article must be seen as a simple pedagogical introduction to Herlihy's
consensus hierarchy.
