Cartographica imports the shapes, databases, and projection information from an ESRI shape file. However, no project or layer styling information is currently imported.
For import, this means that you should (at a minimum) keep around the files that end in:
|SHX||shape index file|
|DBF||database file (containing column data)|
|PRJ||projection file (contains CRS information)|
|CPG||character set file (optional)|
Any other associated files are currently ignored by Cartographica.