  We present early-time ($t < +50$ days) observations of SN 2019muj (=
ASASSN-19tr), one of the best-observed members of the peculiar SN Iax class.
Ultraviolet and optical photometric and optical and near-infrared spectroscopic
follow-up started from $\sim$5 days before maximum light ($t_{max}(B)$ on
$58707.8$ MJD) and covers the photospheric phase. The early observations allow
us to estimate the physical properties of the ejecta and characterize the
possible divergence from a uniform chemical abundance structure. The estimated
bolometric light curve peaks at 1.05 $\times$ 10$^{42}$ erg s$^{-1}$ and
indicates that only 0.031 $M_\odot$ of $^{56}$Ni was produced, making SN
2019muj a moderate luminosity object in the Iax class with peak absolute
magnitude of $M_{V}$ = -16.4 mag. The estimated date of explosion is $t_0 =
58698.2$ MJD and implies a short rise time of $t_{rise}$ = 9.6 days in
$B$-band. We fit of the spectroscopic data by synthetic spectra, calculated via
the radiative transfer code TARDIS. Adopting the partially stratified abundance
template based on brighter SNe Iax provides a good match with SN 2019muj.
However, without earlier spectra, the need for stratification cannot be stated
in most of the elements, except carbon, which is allowed to appear in the outer
layers only. SN 2019muj provides a unique opportunity to link extremely
low-luminosity SNe Iax to well-studied, brighter SNe Iax.
