  To understand the evolution of dust properties in molecular clouds in the
course of the star formation process, we constrain the changes in the dust
emissivity index from star-forming filaments to prestellar and protostellar
cores to T Tauri stars. Using the NIKA2 continuum camera on the IRAM 30~m
telescope, we observed the Taurus B211/B213 filament at 1.2\,mm and 2\,mm with
unprecedented sensitivity and used the resulting maps to derive the dust
emissivity index $\beta$. Our sample of 105 objects detected in the $\beta$ map
of the B211/B213 filament indicates that, overall, $\beta$ decreases from
filament and prestellar cores ($\beta \sim 2\pm0.5$) to protostellar cores
($\beta \sim 1.2 \pm 0.2$) to T-Tauri protoplanetary disk ($\beta < 1$). The
averaged dust emissivity index $\beta$ across the B211/B213 filament exhibits a
flat ($\beta \sim 2\pm0.3$) profile. This may imply that dust grain sizes are
rather homogeneous in the filament, start to grow significantly in size only
after the onset of the gravitational contraction/collapse of prestellar cores
to protostars, reaching big sizes in T Tauri protoplanetary disks. This
evolution from the parent filament to T-Tauri disks happens on a timescale of
about 1-2~Myr.
