  The origin of carbon-enhanced metal-poor (CEMP) stars and their possible
connection with the chemical elements produced by the first stellar generation
is still highly debated. In contrast to the Galactic halo, not many CEMP stars
have been found in the dwarf spheroidal galaxies around the Milky Way. Here we
present detailed abundances from ESO VLT/UVES high-resolution spectroscopy for
ET0097, the first CEMP star found in the Sculptor dwarf spheroidal. This star
has $\text{[Fe/H]}=-2.03\pm0.10$, $\text{[C/Fe]}=0.51\pm0.10$ and
$\text{[N/Fe]}=1.18\pm0.20$. The traditional definition of CEMP stars is
$\text{[C/Fe]}\geq0.70$, but taking into account that this luminous red giant
branch star has undergone mixing, it was intrinsically less nitrogen enhanced
and more carbon-rich when it was formed, and so it falls under the definition
of CEMP stars, as proposed by Aoki et al. (2007) to account for this effect. By
making corrections for this mixing, we conclude that the star had
$\text{[C/Fe]}\approx0.8$ during its earlier evolutionary stages. Apart from
the enhanced C and N abundances, ET0097 shows no peculiarities in other
elements lighter than Zn, and no enhancement of the heavier neutron-capture
elements (Ba, La, Ce, Nd, Sm, Eu, Dy), making this a CEMP-no star. However, the
star does show signs of the weak $r$-process, with an overabundance of the
lighter neutron-capture elements (Sr, Y, Zr). To explain the abundance pattern
observed in ET0097, we explore the possibility that this star was enriched by
primordial stars. In addition to the detailed abundances for ET0097, we present
estimates and upper limits for C abundances in 85 other stars in Sculptor
derived from CN molecular lines, including 11 stars with $\text{[Fe/H]}\leq-2$.
Combining these limits with observations from the literature, the fraction of
CEMP-no stars in Sculptor seems to be significantly lower than in the Galactic
halo.
