diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index c1c78643..eef91dfe 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -47,7 +47,7 @@ repos:
     args: [--include-version-classifiers, --max-py-version=3.10]
 
 - repo: https://github.com/pre-commit/mirrors-mypy
-  rev: v0.971
+  rev: v0.981
   hooks:
   - id: mypy
     name: mypy 3.7 on cibuildwheel/
diff --git a/cibuildwheel/architecture.py b/cibuildwheel/architecture.py
index a922f6f5..90d30c58 100644
--- a/cibuildwheel/architecture.py
+++ b/cibuildwheel/architecture.py
@@ -114,6 +114,7 @@ class Architecture(Enum):
         return all_archs_map[platform]
 
     @staticmethod
+    # pylint: disable-next=inconsistent-return-statements
     def bitness_archs(platform: PlatformName, bitness: Literal["64", "32"]) -> set[Architecture]:
         archs_32 = {Architecture.i686, Architecture.x86}
         auto_archs = Architecture.auto_archs(platform)
diff --git a/cibuildwheel/typing.py b/cibuildwheel/typing.py
index 3ffa5476..6c8fe9fc 100644
--- a/cibuildwheel/typing.py
+++ b/cibuildwheel/typing.py
@@ -3,7 +3,7 @@ from __future__ import annotations
 import os
 import subprocess
 import sys
-from typing import TYPE_CHECKING, NoReturn, Set, Union
+from typing import TYPE_CHECKING, Union
 
 if sys.version_info < (3, 8):
     from typing_extensions import Final, Literal, OrderedDict, Protocol, TypedDict
@@ -11,9 +11,9 @@ else:
     from typing import Final, Literal, OrderedDict, Protocol, TypedDict
 
 if sys.version_info < (3, 11):
-    from typing_extensions import NotRequired
+    from typing_extensions import NotRequired, assert_never
 else:
-    from typing import NotRequired
+    from typing import NotRequired, assert_never
 
 __all__ = (
     "Final",
@@ -25,10 +25,8 @@ __all__ = (
     "PLATFORMS",
     "PopenBytes",
     "Protocol",
-    "Set",
     "TypedDict",
     "OrderedDict",
-    "Union",
     "assert_never",
     "NotRequired",
 )
@@ -44,7 +42,3 @@ else:
 
 PlatformName = Literal["linux", "macos", "windows"]
 PLATFORMS: Final[set[PlatformName]] = {"linux", "macos", "windows"}
-
-
-def assert_never(value: NoReturn) -> NoReturn:
-    assert False, f"Unhandled value: {value} ({type(value).__name__})"  # noqa: B011