Why does multiprocessing raise `AttributeError` for monkey patching?

Question

I'm confused about monkey patching in multiprocessing.Pool. The patching worked before pooling, but the method lost in the pool. I know it could be fixed by overriding or modifying TestClass.test = func to TestClass.func = func

from multiprocessing import Pool

class TestClass:
    def __init__(self) -> None:
        pass

def func(self, a):
    print(a)

# monkey patching
TestClass.test = func
print('test monkey')
TestClass().test(True)

pool = Pool()
for i in range(2):
    temp = TestClass()
    print(f"monkey before pool has test [{bool(hasattr(temp, 'test'))}]")
    pool.apply_async(temp.test, args=(i,))
pool.close()
pool.join()

The Traceback told me func lost?

❯ python monky_patch_multiprocessing.py
test monkey
True
monkey before pool has test [True]
monkey before pool has test [True]
Process ForkPoolWorker-1:
Process ForkPoolWorker-2:
Traceback (most recent call last):
  File "/path/to/miniconda3/envs/seismic/lib/python3.10/multiprocessing/process.py", line 315, in _bootstrap
    self.run()
  File "/path/to/miniconda3/envs/seismic/lib/python3.10/multiprocessing/process.py", line 108, in run
    self._target(*self._args, **self._kwargs)
  File "/path/to/miniconda3/envs/seismic/lib/python3.10/multiprocessing/pool.py", line 114, in worker
    task = get()
  File "/path/to/miniconda3/envs/seismic/lib/python3.10/multiprocessing/queues.py", line 368, in get
    return _ForkingPickler.loads(res)
AttributeError: 'TestClass' object has no attribute 'func'
Traceback (most recent call last):
  File "/path/to/miniconda3/envs/seismic/lib/python3.10/multiprocessing/process.py", line 315, in _bootstrap
    self.run()
  File "/path/to/miniconda3/envs/seismic/lib/python3.10/multiprocessing/process.py", line 108, in run
    self._target(*self._args, **self._kwargs)
  File "/path/to/miniconda3/envs/seismic/lib/python3.10/multiprocessing/pool.py", line 114, in worker
    task = get()
  File "/path/to/miniconda3/envs/seismic/lib/python3.10/multiprocessing/queues.py", line 368, in get
    return _ForkingPickler.loads(res)
AttributeError: 'TestClass' object has no attribute 'func'