diff --git a/django-stubs/core/checks/registry.pyi b/django-stubs/core/checks/registry.pyi
index 12c560e..aa42e54 100644
--- a/django-stubs/core/checks/registry.pyi
+++ b/django-stubs/core/checks/registry.pyi
@@ -15,17 +15,19 @@ class Tags:
     translation: str = ...
     urls: str = ...
 
+_CheckCallable = Callable[..., List[CheckMessage]]
+
 class CheckRegistry:
     registered_checks: Set[Callable] = ...
     deployment_checks: Set[Callable] = ...
     def __init__(self) -> None: ...
-    def register(self, check: Optional[Union[Callable, str]] = ..., *tags: Any, **kwargs: Any) -> Callable: ...
+    def register(self, check: Optional[Union[_CheckCallable, str]] = ..., *tags: str, **kwargs: Any) -> Callable: ...
     def run_checks(
         self,
         app_configs: Optional[List[AppConfig]] = ...,
         tags: Optional[List[str]] = ...,
         include_deployment_checks: bool = ...,
-    ) -> Union[List[CheckMessage], List[int], List[str]]: ...
+    ) -> List[CheckMessage]: ...
     def tag_exists(self, tag: str, include_deployment_checks: bool = ...) -> bool: ...
     def tags_available(self, deployment_checks: bool = ...) -> Set[str]: ...
     def get_checks(self, include_deployment_checks: bool = ...) -> List[Callable]: ...