The Cygwin API library found in the winsup subdirectory of the source code is covered by the GNU Lesser General Public License (LGPL) version 3 or later. For details of the requirements of LGPLv3, please read the GNU Lesser General Public License (LGPL).
Cygwin™ Linking Exception
As a special exception, the copyright holders of the Cygwin library grant you additional permission to link libcygwin.a, crt0.o, and gcrt0.o with independent modules to produce an executable, and to convey the resulting executable under terms of your choice, without any need to comply with the conditions of LGPLv3 section 4. An independent module is a module which is not itself based on the Cygwin library.