  Our main result is a recognition principle for iterated suspensions as
coalgebras over the little disks operads. Given a topological operad, we
construct a comonad in pointed topological spaces endowed with the wedge
product. We then prove an approximation theorem that shows that the comonad
associated to the little $n$-cubes operad is weakly equivalent to the comonad
$\Sigma^n \Omega^n$ arising from the suspension-loop space adjunction. Finally,
our recognition theorem states that every little $n$-cubes coalgebra is
homotopy equivalent to an $n$-fold suspension. These results are the
Eckmann--Hilton dual of May's foundational results on iterated loop spaces.
