  Manganese (Mn) abundances are sensitive probes of the progenitors of Type Ia
supernovae (SNe). In this work, we present a catalog of manganese abundances in
dwarf spheroidal satellites of the Milky Way, measured using medium-resolution
spectroscopy. Using a simple chemical evolution model, we infer the manganese
yield of Type Ia SNe in the Sculptor dwarf spheroidal galaxy (dSph) and compare
to theoretical yields. The sub-solar yield from Type Ia SNe
($\mathrm{[Mn/Fe]}_{\mathrm{Ia}}=-0.30_{-0.03}^{+0.03}$ at
$\mathrm{[Fe/H]}=-1.5$ dex, with negligible dependence on metallicity) implies
that sub-Chandrasekhar-mass (sub-$M_{\mathrm{Ch}}$) white dwarf progenitors are
the dominant channel of Type Ia SNe at early times in this galaxy, although
some fraction ($\gtrsim20\%$) of $M_{\mathrm{Ch}}$ Type Ia or Type Iax SNe are
still needed to produce the observed yield. However, this result does not hold
in all environments. In particular, we find that dSph galaxies with extended
star formation histories (Leo I, Fornax dSphs) appear to have higher [Mn/Fe] at
a given metallicity than galaxies with early bursts of star formation (Sculptor
dSph), suggesting that $M_{\mathrm{Ch}}$ progenitors may become the dominant
channel of Type Ia SNe at later times in a galaxy's chemical evolution.
