diff -rupN --no-dereference Python-3.10.9/Modules/_multiprocessing/semaphore.c Python-3.10.9-new/Modules/_multiprocessing/semaphore.c
--- Python-3.10.9/Modules/_multiprocessing/semaphore.c	2022-12-06 19:31:21.000000000 +0100
+++ Python-3.10.9-new/Modules/_multiprocessing/semaphore.c	2022-12-08 09:37:00.242024881 +0100
@@ -8,6 +8,9 @@
  */
 
 #include "multiprocessing.h"
+#ifdef __MINGW32__
+#include <semaphore.h>
+#endif
 
 enum { RECURSIVE_MUTEX, SEMAPHORE };
 
diff -rupN --no-dereference Python-3.10.9/setup.py Python-3.10.9-new/setup.py
--- Python-3.10.9/setup.py	2022-12-08 09:37:00.234024881 +0100
+++ Python-3.10.9-new/setup.py	2022-12-08 09:37:00.243024881 +0100
@@ -1888,6 +1888,7 @@ class PyBuildExt(build_ext):
 
     def detect_multiprocessing(self):
         # Richard Oudkerk's multiprocessing module
+        multiproc_libs = []
         if MS_WINDOWS:
             multiprocessing_srcs = ['_multiprocessing/multiprocessing.c',
                                     '_multiprocessing/semaphore.c']
@@ -1896,8 +1897,10 @@ class PyBuildExt(build_ext):
             if (sysconfig.get_config_var('HAVE_SEM_OPEN') and not
                 sysconfig.get_config_var('POSIX_SEMAPHORES_NOT_ENABLED')):
                 multiprocessing_srcs.append('_multiprocessing/semaphore.c')
+            if HOST_PLATFORM.startswith(('mingw', 'win')):
+                multiproc_libs += ['ws2_32']
         self.add(Extension('_multiprocessing', multiprocessing_srcs,
-                           include_dirs=["Modules/_multiprocessing"]))
+                           include_dirs=["Modules/_multiprocessing"], libraries=multiproc_libs))
 
         if (not MS_WINDOWS and
            sysconfig.get_config_var('HAVE_SHM_OPEN') and