my mac will not update

Connect to charger. Shutdown. Startup and Immediately Hold Shift Key. This is Safe Mode and will take longer to boot. If all goes well, the installer will process. Note: Since you say this is an Upgrade to New Catalina, the upgrade process may require multiple automatic restarts. Just give it time until the Log-In screen appears

from my personal experience, sometimes upgrading an OSX could be on server's end, not your MacBook, i noticed that High Sierra had that problem were i could not upgrade and stop in the middle then install a few hours later.

i would wait until later.

hope this helped.