Kate, KWrite and KatePart are bundled with the normal KDE releases. If you wish to install any of it, please just install the corresponding KDE packages. KatePart is contained in the kdelibs package, Kate and KWrite in kdebase. If you use a distribution which splits these packages, like Gentoo, Debian or Ubuntu, you can just install the “kate” or “kwrite” packages to get these applications and all required libraries.