  We present the relation between galaxy structure and spectral type, using a
K-selected galaxy sample at 0.5<z<2.0. Based on similarities between the
UV-to-NIR spectral energy distributions, we classify galaxies into 32 spectral
types. The different types span a wide range in evolutionary phases, and thus
-- in combination with available CANDELS/F160W imaging -- are ideal to study
the structural evolution of galaxies. Effective radii (R_e) and Sersic
parameters (n) have been measured for 572 individual galaxies, and for each
type, we determine R_e at fixed stellar mass by correcting for the mass-size
relation. We use the rest-frame U-V vs. V-J diagram to investigate evolutionary
trends. When moving into the direction perpendicular to the star-forming
sequence, in which we see the Halpha equivalent width and the specific star
formation rate (sSFR) decrease, we find a decrease in R_e and an increase in n.
On the quiescent sequence we find an opposite trend, with older redder galaxies
being larger. When splitting the sample into redshift bins, we find that young
post-starburst galaxies are most prevalent at z>1.5 and significantly smaller
than all other galaxy types at the same redshift. This result suggests that the
suppression of star formation may be associated with significant structural
evolution at z>1.5. At z<1, galaxy types with intermediate sSFRs
(10^{-11.5}-10^{-10.5} yr^-1) do not have post-starburst SED shapes. These
galaxies have similar sizes as older quiescent galaxies, implying that they can
passively evolve onto the quiescent sequence, without increasing the average
size of the quiescent galaxy population.
