diff --git a/pandas/core/apply.py b/pandas/core/apply.py
index c04d0821fffdc..199382deadfc3 100644
--- a/pandas/core/apply.py
+++ b/pandas/core/apply.py
@@ -32,6 +32,7 @@
     AggObjType,
     Axis,
     NDFrameT,
+    npt,
 )
 from pandas.util._decorators import cache_readonly
 from pandas.util._exceptions import find_stack_level
@@ -584,18 +585,17 @@ def normalize_dictlike_arg(
                 cols_sorted = list(safe_sort(list(cols)))
                 raise KeyError(f"Column(s) {cols_sorted} do not exist")
 
-        is_aggregator = lambda x: isinstance(x, (list, tuple, dict))
+        aggregator_types = (list, tuple, dict)
 
         # if we have a dict of any non-scalars
         # eg. {'A' : ['mean']}, normalize all to
         # be list-likes
         # Cannot use func.values() because arg may be a Series
-        if any(is_aggregator(x) for _, x in func.items()):
+        if any(isinstance(x, aggregator_types) for _, x in func.items()):
             new_func: AggFuncTypeDict = {}
             for k, v in func.items():
-                if not is_aggregator(v):
-                    # mypy can't realize v is not a list here
-                    new_func[k] = [v]  # type: ignore[list-item]
+                if not isinstance(v, aggregator_types):
+                    new_func[k] = [v]
                 else:
                     new_func[k] = v
             func = new_func
@@ -1079,6 +1079,7 @@ def apply(self) -> DataFrame | Series:
             # if we are a string, try to dispatch
             return self.apply_str()
 
+        # self.f is Callable
         return self.apply_standard()
 
     def agg(self):
@@ -1116,7 +1117,8 @@ def apply_empty_result(self) -> Series:
         )
 
     def apply_standard(self) -> DataFrame | Series:
-        f = self.f
+        # caller is responsible for ensuring that f is Callable
+        f = cast(Callable, self.f)
         obj = self.obj
 
         with np.errstate(all="ignore"):
@@ -1129,14 +1131,9 @@ def apply_standard(self) -> DataFrame | Series:
                 mapped = obj._values.map(f)
             else:
                 values = obj.astype(object)._values
-                # error: Argument 2 to "map_infer" has incompatible type
-                # "Union[Callable[..., Any], str, List[Union[Callable[..., Any], str]],
-                # Dict[Hashable, Union[Union[Callable[..., Any], str],
-                # List[Union[Callable[..., Any], str]]]]]"; expected
-                # "Callable[[Any], Any]"
                 mapped = lib.map_infer(
                     values,
-                    f,  # type: ignore[arg-type]
+                    f,
                     convert=self.convert_dtype,
                 )
 
@@ -1205,7 +1202,7 @@ def transform(self):
 
 def reconstruct_func(
     func: AggFuncType | None, **kwargs
-) -> tuple[bool, AggFuncType | None, list[str] | None, list[int] | None]:
+) -> tuple[bool, AggFuncType | None, list[str] | None, npt.NDArray[np.intp] | None]:
     """
     This is the internal function to reconstruct func given if there is relabeling
     or not and also normalize the keyword to get new order of columns.
@@ -1232,7 +1229,7 @@ def reconstruct_func(
     relabelling: bool, if there is relabelling or not
     func: normalized and mangled func
     columns: list of column names
-    order: list of columns indices
+    order: array of columns indices
 
     Examples
     --------
@@ -1244,7 +1241,7 @@ def reconstruct_func(
     """
     relabeling = func is None and is_multi_agg_with_relabel(**kwargs)
     columns: list[str] | None = None
-    order: list[int] | None = None
+    order: npt.NDArray[np.intp] | None = None
 
     if not relabeling:
         if isinstance(func, list) and len(func) > len(set(func)):
@@ -1291,7 +1288,9 @@ def is_multi_agg_with_relabel(**kwargs) -> bool:
     )
 
 
-def normalize_keyword_aggregation(kwargs: dict) -> tuple[dict, list[str], list[int]]:
+def normalize_keyword_aggregation(
+    kwargs: dict,
+) -> tuple[dict, list[str], npt.NDArray[np.intp]]:
     """
     Normalize user-provided "named aggregation" kwargs.
     Transforms from the new ``Mapping[str, NamedAgg]`` style kwargs
@@ -1345,9 +1344,7 @@ def normalize_keyword_aggregation(kwargs: dict) -> tuple[dict, list[str], list[i
 
     # get the new index of columns by comparison
     col_idx_order = Index(uniquified_aggspec).get_indexer(uniquified_order)
-    # error: Incompatible return value type (got "Tuple[defaultdict[Any, Any],
-    # Any, ndarray]", expected "Tuple[Dict[Any, Any], List[str], List[int]]")
-    return aggspec, columns, col_idx_order  # type: ignore[return-value]
+    return aggspec, columns, col_idx_order
 
 
 def _make_unique_kwarg_list(