Is the process of rebuilding the Brisk Menu, to add a category such as "Internet" or "Graphic", a task which is considered part of the underlying Ubuntu OS, or is it considered part of the Display Manager.
I ask because, after installing first MATE Desktop (on top of Ubuntu Server), then Firefox or Gimp on the Ubuntu server, there is no category listed for either "Internet" or "Graphics" !!!
Not sure if this will help, but you could try:
sudo update-desktop-database
Thank you for responding, Dave, but that utility (along with other tools in the "desktop-file-utils" package) are addressing an issue at a much lower level than what I am trying to deal with.
My issue is how does the OS handle the installation of a new application (Firefox, GIMP) such that once installed, along with any well-formed "*.desktop" file,
how does it create the Brisk Menu category heading "Internet" (if missing, which in my case it is), and
how and where does it place that "*.desktop" file such that it is "plugged-in" to that Brisk Menu structure
for subsequent visibility when you press on the Roundel Icon on the Panel, and offer the newly added selection (Firefox) in the expected "pop-up" window-pane that lists all the "launchers" for the various installed Applications (in this case, specifically, Firefox)?
Under installed files for
there is the following file listed:
That "BriskMenuFactory" is a strong hint of something which I can't seem to locate when searching on "Description and Name" within Synaptic. 
After you’ve installed the app, is their any reason you can’t use the “Menu Editor” tool Main Menu in the Control Center to create any missing categories and make the menu item? That would seem to be the highest level.
Thank you, Walter (?). I appreciate the suggestion. I was aware of that tool, and that I could do all the required edits and "customization" manually.
However, I don't want to do that, because that would imply requiring Users to replicate my attempts to "automate" tasks for a custom build (Ubuntu-Server + MATE Desktop + reduced User-selected set of Apps), then I will have to abandon the attempt to come up with at UbuntuMATE-like alternate that could step in if UbuntuMATE were to become "frozen", as a flavour, for lack of development.
Under UbuntuMATE, the process would somehow automatically add a missing category, then deposit the App-specific launcher in the required menu "slot".
I'm trying to find the specific mechanism I need to install as the first Application after the server OS base followed by the MATE Desktop install.
Being easily prone to intriguing rabbit holes, I did a little research. (Disclaimer: I'm an amateur, so verify this info for yourself before you do something irreparable.)
It seems the various categories that appear in the menus differ slightly for each menu. For example, my Brisk menu has a top-level Administration category, but the Compact menu provides the Administration category as a cascaded second-level category under the System category.
Apparently, the structure (category-wise) of the various MATE menus is controlled by the ".menu" files in /etc/xdg/menus/. As I understand the process, these ".menu" definition files are created/installed by the mate-menus package. Can you check that this package has been installed?
Even when those ".menu" files exist, a particular application's ".desktop" file can override the menu category in which it will appear, or even prevent it from being shown at all. Do you know whether you get the same ".desktop" file regardless of whether Firefox is being installed on Ubuntu server or Ubuntu desktop, or is there a conditional branch in the installation process that installs one Firefox ".desktop" if the target is a server and another if the target is a desktop?
Evidently, installing MATE desktop on a non-desktop Ubuntu installation is more complex than I realized. It might be more reliable to start with a non-MATE Ubuntu desktop installation and then switch the DE to MATE, but that may not be compatible with your goals.
So, I've come across the reference to
Looking at the contents of those, I dug around and found various *.directory files located in
Files in "/usr/share/desktop-directories" :
/usr/share/desktop-directories # grep '^Name=' *.directory
ActionGames.directory:Name=Action
AdventureGames.directory:Name=Adventure
ArcadeGames.directory:Name=Arcade
AudioVideo.directory:Name=Sound & Video
BlocksGames.directory:Name=Falling blocks
BoardGames.directory:Name=Board
CardGames.directory:Name=Cards
Debian.directory:Name=Debian
Development.directory:Name=Programming
Education.directory:Name=Education
Game.directory:Name=Games
GnomeScience.directory:Name=Science
Graphics.directory:Name=Graphics
Hardware.directory:Name=Hardware
KidsGames.directory:Name=Kids
LogicGames.directory:Name=Logic
lxde-audio-video.directory:Name=Sound & Video
lxde-debian.directory:Name=Debian
lxde-development.directory:Name=Programming
lxde-education.directory:Name=Education
lxde-game.directory:Name=Games
lxde-graphics.directory:Name=Graphics
lxde-hardware.directory:Name=Hardware
lxde-internet-and-network.directory:Name=Internet and Network
lxde-look-and-feel.directory:Name=Look and Feel
lxde-menu-applications.directory:Name=Applications
lxde-menu-system.directory:Name=System
lxde-network.directory:Name=Internet
lxde-office.directory:Name=Office
lxde-other.directory:Name=Other
lxde-personal.directory:Name=Personal
lxde-science-math.directory:Name=Science & Math
lxde-settings.directory:Name=Preferences
lxde-settings-system.directory:Name=Administration
lxde-system.directory:Name=System
lxde-system-tools.directory:Name=System Tools
lxde-utility-accessibility.directory:Name=Universal Access
lxde-utility.directory:Name=Accessories
matecc.directory:Name=Control Center
mate-screensaver.directory:Name=Screensavers
Network.directory:Name=Internet
Office.directory:Name=Office
Personal.directory:Name=Personal
RolePlayingGames.directory:Name=Role playing
Settings.directory:Name=Preferences
Settings-System.directory:Name=Administration
SimulationGames.directory:Name=Simulation
SportsGames.directory:Name=Sports
StrategyGames.directory:Name=Strategy
System.directory:Name=System
System-Tools.directory:Name=System Tools
Utility-Accessibility.directory:Name=Universal Access
Utility.directory:Name=Accessories
X-GNOME-Menu-Applications.directory:Name=Applications
X-GNOME-Other.directory:Name=Other
X-GNOME-Sundry.directory:Name=Sundry
X-GNOME-SystemSettings.directory:Name=System Settings
X-GNOME-Utilities.directory:Name=Utilities
X-GNOME-WebApplications.directory:Name=Web Applications
Files in "/usr/share/mate/desktop-directories" :
/usr/share/mate/desktop-directories # grep '^Name=' *.directory
mate-audio-video.directory:Name=Sound & Video
mate-collection.directory:Name=Collection
mate-development.directory:Name=Programming
mate-education.directory:Name=Education
mate-game.directory:Name=Games
mate-graphics.directory:Name=Graphics
mate-hardware.directory:Name=Hardware
mate-internet-and-network.directory:Name=Internet and Network
mate-look-and-feel.directory:Name=Look and Feel
mate-menu-applications.directory:Name=Applications
mate-menu-system.directory:Name=System
mate-network.directory:Name=Internet
mate-office.directory:Name=Office
mate-other.directory:Name=Other
mate-personal.directory:Name=Personal
mate-settings.directory:Name=Preferences
mate-settings-system.directory:Name=Administration
mate-system.directory:Name=System
mate-system-tools.directory:Name=System Tools
mate-utility-accessibility.directory:Name=Universal Access
mate-utility.directory:Name=Accessories
Files in "/var/lib/menu-xdg/desktop-directories/menu-xdg" :
/var/lib/menu-xdg/desktop-directories/menu-xdg # grep '^Name=' *.directory
debian-applications-accessibility.directory:Name=Accessibility
debian-applications-data-management.directory:Name=Data Management
debian-applications.directory:Name=Applications
debian-applications-editors.directory:Name=Editors
debian-applications-graphics.directory:Name=Graphics
debian-applications-network-communication.directory:Name=Communication
debian-applications-network.directory:Name=Network
debian-applications-network-file-transfer.directory:Name=File Transfer
debian-applications-network-web-browsing.directory:Name=Web Browsing
debian-applications-programming.directory:Name=Programming
debian-applications-science.directory:Name=Science
debian-applications-science-mathematics.directory:Name=Mathematics
debian-applications-shells.directory:Name=Shells
debian-applications-sound.directory:Name=Sound
debian-applications-system-administration.directory:Name=Administration
debian-applications-system.directory:Name=System
debian-applications-system-hardware.directory:Name=Hardware
debian-applications-system-monitoring.directory:Name=Monitoring
debian-applications-system-package-management.directory:Name=Package Management
debian-applications-system-security.directory:Name=Security
debian-applications-text.directory:Name=Text
debian-applications-video.directory:Name=Video
debian-applications-viewers.directory:Name=Viewers
debian-games-action.directory:Name=Action
debian-games.directory:Name=Games
debian-games-toys.directory:Name=Toys
debian-help.directory:Name=Help