  Quiescence in galaxies correlates strongly with the central
density/morphology of the stellar distribution. We investigate two possible
explanations for this morphology-quiescence relation: 1) the central density
results from a dissipative core-building event ("compaction") that feeds an AGN
that quenches the galaxy and 2) the central density results from inside-out
growth by galaxy-wide star formation that is quenched by processes unrelated to
the central density. We aim to distinguish these two scenarios using the MaNGA
survey to determine profiles of stellar age, specific star formation rate
(sSFR) and gas phase metallicity (O/H) as a function of stellar mass surface
density within 1 kpc (Sigma_1kpc) and total stellar mass (M*). We find that
gradients in age, sSFR and O/H depend on the galaxy's position on the
Sigma_1kpc-M* diagram, suggesting at least two evolutionary pathways. The first
pathway consists of galaxies with low Sigma_1kpc for their M* whose centres are
old, metal-rich and suppressed in sSFR compared to their outskirts, consistent
with the inside-out growth scenario. The second pathway, consistent with a
compaction-like core-building scenario, consists of galaxies with higher
Sigma_1kpc for their M*, whose centres are younger, enhanced in sSFR and
metal-deficient compared to their outskirts. Moreover, the WISE-selected AGN
fraction peaks in the same area of the Sigma_1kpc-M* diagram as the
core-building pathway. The sSFR profiles of the quiescent population suggest
that galaxies on the compaction-like path quench uniformly, while those on the
inside-out growing path quench their centres first. Our results imply that both
pathways contribute to the morphology-quiescence relation.
