software and OS upgrades
What is my upgrade path if i have a late 2013 iMac that is running macOS High Sierra 10.13.6?
iMac Pro
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Only these 2 later OSes will run on the 20132 iMac...
macOS Mojave 10.14.6 - Technical Specifications
General Requirements
OS X 10.8 or later
2GB of memory
12.5GB of available storage (OS X El Capitan 10.11.5 or later)*
Some features require an Apple ID; terms apply.
Some features require a compatible Internet service provider; fees may apply.
Mac Hardware Requirements
For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Mojave:
MacBook (Early 2015 or newer)
MacBook Air (Mid 2012 or newer)
MacBook Pro (Mid 2012 or newer)
Mac mini (Late 2012 or newer)
iMac (Late 2012 or newer)
iMac Pro (2017)
Mac Pro (Late 2013; Mid 2010 and Mid 2012 models with recommended Metal-capable graphics cards)
Don't use FireFox for these links…
https://itunes.apple.com/us/app/macos-mojave/id1398502828?mt=12
macOS Catalina 10.15.7 - Technical Specifications
General Requirements
OS X 10.9 or later
4GB of memory
12.5GB of available storage (OS X El Capitan 10.11.5 or later)*
Some features require an Apple ID; terms apply.
Some features require a compatible internet service provider; fees may apply.
Mac Hardware Requirements
For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Catalina:
MacBook (Early 2015 or newer)
MacBook Air (Mid 2012 or newer)
MacBook Pro (Mid 2012 or newer)
Mac mini (Late 2012 or newer)
iMac (Late 2012 or newer)
iMac Pro (2017)
Mac Pro (Late 2013 or newer)
https://support.apple.com/en-us/HT210190
https://apps.apple.com/gb/app/macos-catalina/id1466841314?ls=1&mt=12
How to upgrade to macOS Catalina – Apple Support
And caution on 10.15 or higher, to see which Apps will no longer work in 10.15 get Go64...