Let C be some class of objects equipped with a
set of simplifying moves. When we apply these to a given
object M∈C as long as possible, we get a root of M.
Our main result is that under certain
conditions the root of any object exists and is unique. We apply this
result to different situations and get several new results and new
proofs of known results. Among them there are a new proof of the
Kneser–Milnor prime decomposition theorem for 3–manifolds
and different versions of this theorem for cobordisms, knotted graphs,
and orbifolds.
