first CygWin and MinGW are really NOT linux operating systems
CygWin can RUN some ( about 70 to 80% ) of linux programs on Microsoft Windows
BUT ( and this is a VERY BIG ONE) it uses a emulatio0n DLL "cygwin1.dll" and everything has to pass through that ONE file
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MinGW BUILDS!!!!! linux source code into MICROSOFT!!!! .exe files and by using "dlltool" can convert the linux "so" files to MICROSOFT.dll's
but it also can only build about 70% to 80% of Linux code
I take it you have NOT READ the very VAST amount of documents on the cygwin website
https://www.cygwin.com/
and there is a even LARGER amount of documentation and guides
type " cygwin " into google and hit enter
mind you cygwin is TERMINAL ONLY !!!
there are NO gui's
no graphics
just the text ONLY terminal
for graphics you need to install X and a desktop
http://x.cygwin.com/