Kate is part of the KDE project http://www.kde.org/.
Kate can be found in the kdesdk package on ftp://ftp.kde.org/pub/kde/, the main FTP site of the KDE project.
For detailed information on how to compile and install KDE applications see Building and Running KDE Software From Source
Since KDE uses cmake you should have no trouble compiling it. Should you run into problems please report them to the KDE mailing lists.