Hello gyroscope,
Thank you for using the Apple Support Communities! We understand you are running to a 'PKDownload error 12' while installing macOS Catalina and are happy to help.
Typically, this is a result of some kind of network issue. We would like to first have you restart your Mac and then try to install macOS Catalina again: How to turn your Mac on or off - Apple Support. If this does not help, please try the below steps next.
-Test with any third-party firewall / security / networking software temporarily removed/disabled.
-Test with a wired connection to your router, if possible.
-If a wired connection is not possible, check for potential sources of wireless interference: Resolve Wi-Fi and Bluetooth issues caused by wireless interference - Apple Support and Recommended settings for Wi-Fi routers and access points - Apple Support.
-Try restarting your router / modem (unplugging them for 30 seconds then plugging them back in).
If the issue persists, please try downloading and installing macOS Catalina on a different network.
If you need continued support after these steps, reach back out with an update.
Best regards.