  We present spatially-resolved two-dimensional maps and radial trends of the
stellar populations and kinematics for a sample of six compact elliptical
galaxies (cE) using spectroscopy from the Keck Cosmic Web Imager (KCWI). We
recover their star formation histories, finding that all except one of our cEs
are old and metal rich, with both age and metallicity decreasing toward their
outer radii. We also use the integrated values within one effective radius to
study different scaling relations. Comparing our cEs with others from the
literature and from simulations we reveal the formation channel that these
galaxies might have followed. All our cEs are fast rotators, with relatively
high rotation values given their low ellipticites. In general, the properties
of our cEs are very similar to those seen in the cores of more massive
galaxies, and in particular, to massive compact galaxies. Five out of our six
cEs are the result of stripping a more massive (compact or extended) galaxy,
and only one cE is compatible with having been formed intrinsically as the
low-mass, compact object that we see today. These results further confirm that
cEs are a mixed-bag of galaxies that can be formed following different
formation channels, reporting for the first time an evolutionary link within
the realm of compact galaxies (at all stellar masses).
