  In arXiv:math/0606241v2 M. Kontsevich and Y. Soibelman argue that the
category of noncommutative (thin) schemes is equivalent to the category of
coalgebras. We propose that under this correspondence the affine scheme of a
k-algebra A is the dual coalgebra A^o and draw some consequences. In
particular, we describe the dual coalgebra A^o of A in terms of the A-infinity
structure on the Yoneda-space of all the simple finite dimensional
A-representations.
