  Using the Sloan Digital Sky Survey, we adopt the sSFR-$\Sigma_{1kpc}$ diagram
as a diagnostic tool to understand quenching in different environments. sSFR is
the specific star formation rate, and $\Sigma_{1kpc}$ is the stellar surface
density in the inner kpc. Although both the host halo mass and group-centric
distance affect the satellite population, we find that these can be
characterised by a single number, the quenched fraction, such that key features
of the sSFR-$\Sigma_{1kpc}$ diagram vary smoothly with this proxy for the
"environment". Particularly, the sSFR of star-forming galaxies decreases
smoothly with this quenched fraction, the sSFR of satellites being 0.1 dex
lower than in the field. Furthermore, $\Sigma_{1kpc}$ of the transition
galaxies (i.e., the "green valley" or GV) decreases smoothly with the
environment, by as much as 0.2 dex for $M_* = 10^{9.75-10} M_{\odot}$ from the
field, and decreasing for satellites in larger halos and at smaller radial
distances within same-mass halos. We interpret this shift as indicating the
relative importance of today's field quenching track vs. the cluster quenching
track. These environmental effects in the sSFR-$\Sigma_{1kpc}$ diagram are most
significant in our lowest mass range ($9.75 < \log M_{*}/M_{\odot} < 10$). One
feature that is shared between all environments is that at a given $M_{*}$
quenched galaxies have about 0.2-0.3 dex higher $\Sigma_{1kpc}$ than the
star-forming population. These results indicate that either $\Sigma_{1kpc}$
increases (subsequent to satellite quenching), or $\Sigma_{1kpc}$ for
individual galaxies remains unchanged, but the original $M_*$ or the time of
quenching is significantly different from those now in the GV.
