Kate is part of the KDE project http://www.kde.org/.

Kate can be found in the kdebase package on ftp://ftp.kde.org/pub/kde/, the main FTP site of the KDE project.

In order to compile and install Kate on your system, type the following in the base directory of the Kate distribution:

% ./configure
% make
% make install

Since Kate uses autoconf and automake you should have no trouble compiling it. Should you run into problems please report them to the KDE mailing lists.