diff --git a/stdlib/functools.pyi b/stdlib/functools.pyi
index acc45cd42..3003ef061 100644
--- a/stdlib/functools.pyi
+++ b/stdlib/functools.pyi
@@ -1,6 +1,6 @@
 import sys
 import types
-from _typeshed import Self, SupportsAllComparisons, SupportsItems
+from _typeshed import IdentityFunction, Self, SupportsAllComparisons, SupportsItems
 from collections.abc import Callable, Hashable, Iterable, Sequence, Sized
 from typing import Any, Generic, NamedTuple, TypeVar, overload
 from typing_extensions import Literal, TypeAlias, final
@@ -68,7 +68,7 @@ WRAPPER_ASSIGNMENTS: tuple[
 WRAPPER_UPDATES: tuple[Literal["__dict__"]]
 
 def update_wrapper(wrapper: _T, wrapped: _AnyCallable, assigned: Sequence[str] = ..., updated: Sequence[str] = ...) -> _T: ...
-def wraps(wrapped: _AnyCallable, assigned: Sequence[str] = ..., updated: Sequence[str] = ...) -> Callable[[_T], _T]: ...
+def wraps(wrapped: _AnyCallable, assigned: Sequence[str] = ..., updated: Sequence[str] = ...) -> IdentityFunction: ...
 def total_ordering(cls: type[_T]) -> type[_T]: ...
 def cmp_to_key(mycmp: Callable[[_T, _T], int]) -> Callable[[_T], SupportsAllComparisons]: ...
 
diff --git a/stdlib/typing.pyi b/stdlib/typing.pyi
index fee36e626..969e61952 100644
--- a/stdlib/typing.pyi
+++ b/stdlib/typing.pyi
@@ -1,6 +1,6 @@
 import collections  # Needed by aliases like DefaultDict, see mypy issue 2986
 import sys
-from _typeshed import ReadableBuffer, Self as TypeshedSelf, SupportsKeysAndGetItem
+from _typeshed import IdentityFunction, ReadableBuffer, Self as TypeshedSelf, SupportsKeysAndGetItem
 from abc import ABCMeta, abstractmethod
 from types import BuiltinFunctionType, CodeType, FrameType, FunctionType, MethodType, ModuleType, TracebackType
 from typing_extensions import Literal as _Literal, ParamSpec as _ParamSpec, final as _final
@@ -874,7 +874,7 @@ if sys.version_info >= (3, 11):
         kw_only_default: bool = ...,
         field_specifiers: tuple[type[Any] | Callable[..., Any], ...] = ...,
         **kwargs: Any,
-    ) -> Callable[[_T], _T]: ...
+    ) -> IdentityFunction: ...
 
 # Type constructors
 
diff --git a/stdlib/typing_extensions.pyi b/stdlib/typing_extensions.pyi
index b94daaba9..38fb9dec1 100644
--- a/stdlib/typing_extensions.pyi
+++ b/stdlib/typing_extensions.pyi
@@ -1,6 +1,6 @@
 import abc
 import sys
-from _typeshed import Self as TypeshedSelf  # see #6932 for why the alias cannot have a leading underscore
+from _typeshed import IdentityFunction, Self as TypeshedSelf  # see #6932 for why the Self alias cannot have a leading underscore
 from typing import (  # noqa: Y022,Y027,Y039
     TYPE_CHECKING as TYPE_CHECKING,
     Any,
@@ -232,4 +232,4 @@ else:
         kw_only_default: bool = ...,
         field_specifiers: tuple[type[Any] | Callable[..., Any], ...] = ...,
         **kwargs: object,
-    ) -> Callable[[_T], _T]: ...
+    ) -> IdentityFunction: ...
diff --git a/stubs/mypy-extensions/mypy_extensions.pyi b/stubs/mypy-extensions/mypy_extensions.pyi
index 705a56507..bf8d72ba8 100644
--- a/stubs/mypy-extensions/mypy_extensions.pyi
+++ b/stubs/mypy-extensions/mypy_extensions.pyi
@@ -1,6 +1,6 @@
 import abc
-from _typeshed import Self
-from collections.abc import Callable, ItemsView, KeysView, Mapping, ValuesView
+from _typeshed import IdentityFunction, Self
+from collections.abc import ItemsView, KeysView, Mapping, ValuesView
 from typing import Any, Generic, TypeVar, overload
 
 _T = TypeVar("_T")
@@ -54,6 +54,6 @@ class NoReturn: ...
 # a class decorator, but mypy does not support type[_T] for abstract
 # classes until this issue is resolved, https://github.com/python/mypy/issues/4717.
 def trait(cls: _T) -> _T: ...
-def mypyc_attr(*attrs: str, **kwattrs: object) -> Callable[[_T], _T]: ...
+def mypyc_attr(*attrs: str, **kwattrs: object) -> IdentityFunction: ...
 
 class FlexibleAlias(Generic[_T, _U]): ...
diff --git a/stubs/six/six/__init__.pyi b/stubs/six/six/__init__.pyi
index 1c79752e0..79aaf98ba 100644
--- a/stubs/six/six/__init__.pyi
+++ b/stubs/six/six/__init__.pyi
@@ -3,6 +3,7 @@ from __future__ import print_function
 import builtins
 import types
 import unittest
+from _typeshed import IdentityFunction
 from builtins import next as next
 from collections.abc import Callable, ItemsView, Iterable, Iterator as _Iterator, KeysView, Mapping, ValuesView
 from functools import wraps as wraps
@@ -83,7 +84,7 @@ def raise_from(value: BaseException | type[BaseException], from_value: BaseExcep
 print_ = print
 
 def with_metaclass(meta: type, *bases: type) -> type: ...
-def add_metaclass(metaclass: type) -> Callable[[_T], _T]: ...
+def add_metaclass(metaclass: type) -> IdentityFunction: ...
 def ensure_binary(s: bytes | str, encoding: str = ..., errors: str = ...) -> bytes: ...
 def ensure_str(s: bytes | str, encoding: str = ..., errors: str = ...) -> str: ...
 def ensure_text(s: bytes | str, encoding: str = ..., errors: str = ...) -> str: ...