just upgraded to Catalina on late 2013 iMac. I logged in OK, but there is the spinning wait symbol (not the beachball) and my desktop has not appeared. it

A Troubleshooting Procedure that may Fix Problems with macOS El Capitan or Later

You should try each, one at a time, then test to see if the problem is fixed before going on to the next.

    Be sure to backup your files before proceeding if possible.

1. Shutdown the computer, wait 30 seconds, restart the computer.
2. Disconnect all third-party peripherals.
3. Resetting your Mac's PRAM and NVRAM
4. Reset the System Management Controller (SMC)
5. Reset your Startup Disk and Sound preferences, if needed, after resetting the PRAM.
6. Test in safe mode to see if the problem persists, then restart normally. Use safe mode to isolate issues with your Mac and Playing Safe - what does Safe mode do?
7. Repair the disk by booting from the Recovery HD. Immediately after the chime hold down the Command and R keys until the Utility Menu appears. Choose Disk Utility and click on the Continue button. Select the indented (usually, Macintosh HD) volume entry from the side list.  Click on the First Aid button in the toolbar. Wait for the Done button to appear. Quit Disk Utility and return to the Utility Menu. Restart the computer from the Apple Menu.
8. Repair permissions on the Home folder: Resolve issues caused by changing the permissions of items in your home folder.
9. Create a New User Account Open Users & Groups preferences. Click on the lock icon and enter your Admin password when prompted. On the left under Current User click on the Add [+] button under Login Options. Setup a new Admin user account. Upon completion log out of your current account then log into the new account. If your problems cease, then consider switching to the new account and transferring your files to it - Transferring files from one User Account to another.
10. Reinstall OS X by booting from the Recovery HD using the Command and R keys. When the Utility Menu appears select Reinstall OS X then click on the Continue button.
11. Erase and Install OS X Restart the computer. Immediately after the chime hold down the Command and R keys until the Apple logo appears. When the Utility Menu appears:

     1. Select Disk Utility from the Utility Menu and click on the Continue button.

     2. When Disk Utility loads select the drive (out-dented entry) from the Device list.

     3. Click on the Erase icon in Disk Utility's toolbar. A panel will drop down.

     4. Set the Format type to APFS (for SSDs only) or Mac OS Extended (Journaled.)

     5. Click on the Apply button, then wait for the Done button to activate and click on it.

     6. Quit Disk Utility and return to the Utility Menu.

     7. Select Reinstall OS X and click on the Continue button.

Hello Sid_mac!

I like your Sunglaces,on your Imac Profile!

When i get to the Level 2,i also make that Profile,i just think?

Just kidding!

You have just upgrade,to Mac OS Catalina,on your,2013 iMac,but there, are a spinning wait symbol?(Not Beachballing.)

If,you have a Time machine Copy,why not install,the Mac OS Catalina on this?

I had a 2013 iMac,and when it get sluggish,and slow i reinstall the, OSX/ Mac OS!