How can I use Cygwin under Ubuntu?

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http://askubuntu.com – I have written a tiny application for Ubuntu, and it works great. I am interested in cross-compiling it for Windows. I have installed mingw32 from repository, and it compiles simple files very well. However, the app I want to compile for Windows uses some UNIX specific mechanism - for example it makes use of the sys/socket.h file, and the mingw compiler claims it can't find it. One solution is to install Cygwin on a Windows machine, and try compiling the application from there, using Cygwin executables. Unfortunately, I don't have access to any Windows machine, as I don't own a copy that sys (HowTos)