Side by Side operating systems

If you performed a final Time Machine backup of your Mojave installation before upgrading to Catalina, then yes, you can go back to Mojave by booting into Recovery mode ⌘-R, and then choosing Restore from Time Machine Backup. This will simply replace the Catalina installation with Mojave in the same state as it was before the upgrade. You would lose any files created since you upgraded to Catalina unless you move them to another storage medium to save them, and then add those to your Mojave recovery after it reboots.

If you made no Time Machine backup of Mojave before the upgrade, then you are looking at a clean install of Mojave with loss of all current drive contents.

Your 11 inch MacBook Air has neither sufficient RAM, screen size, nor CPU power to drive a virtual machine (e.g. Virtualbox, VMware, or Parallel's Desktop) with macOS as a guest. An 8 GB RAM configuration would be marginal. So that rules out concurrency. If that is a 4GB RAM machine, then it will barely run Catalina or Mojave as either will consume most of that default 4GB RAM without any other application's running.

If you have a 256 GB or larger drive in that Air, you could potentially add another APFS partition for the second operating system as outlined in this document. Ignore references to beta versions of Catalina.

You could install both Catalina and Mojave by means of virtual machine -- see https://appletoolbox.com/need-to-run-32-bit-apps-on-macos-catalina-use-a-mojave-virtual-machine/ for more info. I've not done this myself, so let us know how it works if you get it working.

Good luck...