  The Seebeck and Nernst coefficients $S$ and $\nu$ of the cuprate
superconductor YBa$_2$Cu$_3$O$_y$ (YBCO) were measured in a single crystal with
doping $p = 0.12$ in magnetic fields up to H = 28 T. Down to T=9 K, $\nu$
becomes independent of field by $H \simeq 30$ T, showing that superconducting
fluctuations have become negligible. In this field-induced normal state, $S/T$
and $\nu/T$ are both large and negative in the $T \to 0$ limit, with the
magnitude and sign of $S/T$ consistent with the small electron-like Fermi
surface pocket detected previously by quantum oscillations and the Hall effect.
The change of sign in $S(T)$ at $T \simeq 50$ K is remarkably similar to that
observed in La$_{2-x}$Ba$_x$CuO$_4$, La$_{2-x-y}$Nd$_y$Sr$_x$CuO$_4$ and
La$_{2-x-y}$Eu$_y$Sr$_x$CuO$_4$, where it is clearly associated with the onset
of stripe order. We propose that a similar density-wave mechanism causes the
Fermi surface reconstruction in YBCO.
