  On the AGB, low to intermediate mass stars blow away their outer envelopes,
forming planetary nebulae. Interaction between the planetary nebula and its
central progenitor is poorly understood and even more complex when the central
object is a binary star with a magnetically active component, like it is the
case for IN Com. We aim to quantify the surface activity of the cool binary
component of IN Com and aim to explain its origin. We need a better
understanding of how central binary stars in planetary nebulae evolve and how
this evolution could develop such magnetically active stars like IN Com. We
present 13 Doppler images covering six months in 2017 and use them to measure
the surface differential rotation. Hitherto unpublished photometric data from
between 1989-2017 are presented. We apply Fourier-transformation to both
photometry and spectra. Very high resolution spectra are used to update IN
Com's astrophysical parameters by means of spectral synthesis. Doppler images
show cool and warm spots coexisting with an average surface temperature
contrast of -1000K and +300K with respect to the effective temperature.
Approximately 8% of the surface is covered with cool spots and 3% with warm
spots. A cool polar spot is seen in all images. We found anti-solar surface
differential rotation with a shear coefficient of -0.026+/-0.005 and an
equatorial rotation period of 5.973+/-0.008 d. We reconfirm the 5.9-day
rotation period of the cool star from photometry, radial velocities, and H
alpha line-profile variations. A long-term V-brightness variation with a likely
period of 7.2yr is found. It appears in phase with the orbital radial velocity
of the binary system in the sense brightest at highest velocity and faintest at
lowest velocity. We redetermine [Ba/Fe], [Y/Fe] and [Sr/Fe] ratios and confirm
the overabundance of these s-process elements in the atmosphere of IN Com.
