imac will not update macos 10.15.

Your Wi-Fi connection could be week or slow?

1. Try disconnecting some external devices, especially USB 3.0 external drives and try again.
2. Try connecting the iMac directly to your Router using an Ethernet cable and try again.

Your iMac must have been introduced by Apple in 2012 or later in order to update to Catalina. You can verify this from the menu : About This Mac panel, and in particular, your parenthetical content in the following example's red box:

Try it in Safe Mode...

Safe Boot from the HD, (holding Shift key down at startup), does the problem occur in Safe Mode?