Catalina back to Mojave

Is this for your iMac? If so, which exact model is it? Did it come with macOS Catalina originally or an earlier release? If it came with Catalina, you will not be able to downgrade it. Otherwise, there are a few methods that should be available for you to do so. As such, I suggest giving the following support article a look:

• Revert your Mac to a previous macOS version - Apple Support

If you have a complete TM backup of your Mac when it was running macOS Mojave, then it should be possible to first erase it, and then, re-install Mojave from that backup by using Recovery Mode. I'm assuming, since you stated it came with OS X Yosemite, that it is either a Late 2014 or Mid 2015 model ... correct?

Another option would be to create a bootable installer with macOS Mojave after you erased your Mac.

See if the following support articles can help:

• How to erase an Intel-based Mac - Apple Support
• How to reinstall macOS - Apple Support

Oops, sorry about that. Apple must have just removed it. Let me see if I can find the correct one.

Here you go: How to get old versions of macOS - Apple Support

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