For those unaware, regular Ubuntu will be replacing the ever-aging Ubuntu Software Centre (USC) with GNOME Software Centre. Ubuntu MATE 15.10 doesn't ship with any and gives you this choice in Welcome.
If it is fully compatible, this will ship by default in Ubuntu MATE 16.04 LTS. Welcome will continue to offer alternates.
If you fancy giving it a test run, here's the PPA:
Once installed you’ll need to run this script as root to fetch and populate the app with AppStream data (as of writing, applications still won’t show up. This is a known issue and will be fixed in a later update).
okay, I made it executable and then run it as root in a terminal Alt + F2 > gksudo caja > double click on the downloaded package > "Run in terminal", to run it; open a terminal and type "sudo gnome-software" or "gnome-software" (you will have to enter your password after selecting a package if you use the 2nd command!) and you get this: