diff --git a/pandas/core/base.py b/pandas/core/base.py
index 8c8037091559d..f236fea93278c 100644
--- a/pandas/core/base.py
+++ b/pandas/core/base.py
@@ -634,20 +634,19 @@ def _is_builtin_func(self, arg):
 class ShallowMixin:
     _attributes = []  # type: List[str]
 
-    def _shallow_copy(self, obj=None, obj_type=None, **kwargs):
+    def _shallow_copy(self, obj=None, **kwargs):
         """
         return a new object with the replacement attributes
         """
         if obj is None:
             obj = self._selected_obj.copy()
-        if obj_type is None:
-            obj_type = self._constructor
-        if isinstance(obj, obj_type):
+
+        if isinstance(obj, self._constructor):
             obj = obj.obj
         for attr in self._attributes:
             if attr not in kwargs:
                 kwargs[attr] = getattr(self, attr)
-        return obj_type(obj, **kwargs)
+        return self._constructor(obj, **kwargs)
 
 
 class IndexOpsMixin:
diff --git a/pandas/core/groupby/base.py b/pandas/core/groupby/base.py
index fc3bb69afd0cb..fed387cbeade4 100644
--- a/pandas/core/groupby/base.py
+++ b/pandas/core/groupby/base.py
@@ -11,22 +11,6 @@ class GroupByMixin:
     Provide the groupby facilities to the mixed object.
     """
 
-    @staticmethod
-    def _dispatch(name, *args, **kwargs):
-        """
-        Dispatch to apply.
-        """
-
-        def outer(self, *args, **kwargs):
-            def f(x):
-                x = self._shallow_copy(x, groupby=self._groupby)
-                return getattr(x, name)(*args, **kwargs)
-
-            return self._groupby.apply(f)
-
-        outer.__name__ = name
-        return outer
-
     def _gotitem(self, key, ndim, subset=None):
         """
         Sub-classes to define. Return a sliced object.
diff --git a/pandas/core/window/common.py b/pandas/core/window/common.py
index 2ad5a1eb6faed..3fd567f97edae 100644
--- a/pandas/core/window/common.py
+++ b/pandas/core/window/common.py
@@ -26,7 +26,23 @@
 """
 
 
-class _GroupByMixin(GroupByMixin):
+def _dispatch(name: str, *args, **kwargs):
+    """
+    Dispatch to apply.
+    """
+
+    def outer(self, *args, **kwargs):
+        def f(x):
+            x = self._shallow_copy(x, groupby=self._groupby)
+            return getattr(x, name)(*args, **kwargs)
+
+        return self._groupby.apply(f)
+
+    outer.__name__ = name
+    return outer
+
+
+class WindowGroupByMixin(GroupByMixin):
     """
     Provide the groupby facilities.
     """
@@ -41,9 +57,9 @@ def __init__(self, obj, *args, **kwargs):
         self._groupby.grouper.mutated = True
         super().__init__(obj, *args, **kwargs)
 
-    count = GroupByMixin._dispatch("count")
-    corr = GroupByMixin._dispatch("corr", other=None, pairwise=None)
-    cov = GroupByMixin._dispatch("cov", other=None, pairwise=None)
+    count = _dispatch("count")
+    corr = _dispatch("corr", other=None, pairwise=None)
+    cov = _dispatch("cov", other=None, pairwise=None)
 
     def _apply(
         self, func, name=None, window=None, center=None, check_minp=None, **kwargs
@@ -53,6 +69,7 @@ def _apply(
         performing the original function call on the grouped object.
         """
 
+        # TODO: can we de-duplicate with _dispatch?
         def f(x, name=name, *args):
             x = self._shallow_copy(x)
 
diff --git a/pandas/core/window/expanding.py b/pandas/core/window/expanding.py
index 47bd8f2ec593b..55389d2fc7d9f 100644
--- a/pandas/core/window/expanding.py
+++ b/pandas/core/window/expanding.py
@@ -3,7 +3,7 @@
 from pandas.compat.numpy import function as nv
 from pandas.util._decorators import Appender, Substitution
 
-from pandas.core.window.common import _doc_template, _GroupByMixin, _shared_docs
+from pandas.core.window.common import WindowGroupByMixin, _doc_template, _shared_docs
 from pandas.core.window.rolling import _Rolling_and_Expanding
 
 
@@ -250,7 +250,7 @@ def corr(self, other=None, pairwise=None, **kwargs):
         return super().corr(other=other, pairwise=pairwise, **kwargs)
 
 
-class ExpandingGroupby(_GroupByMixin, Expanding):
+class ExpandingGroupby(WindowGroupByMixin, Expanding):
     """
     Provide a expanding groupby implementation.
     """
diff --git a/pandas/core/window/rolling.py b/pandas/core/window/rolling.py
index bf5ea9c457e8a..75f9a1c628d72 100644
--- a/pandas/core/window/rolling.py
+++ b/pandas/core/window/rolling.py
@@ -39,9 +39,9 @@
 import pandas.core.common as com
 from pandas.core.index import Index, ensure_index
 from pandas.core.window.common import (
+    WindowGroupByMixin,
     _doc_template,
     _flex_binary_moment,
-    _GroupByMixin,
     _offset,
     _require_min_periods,
     _shared_docs,
@@ -1917,7 +1917,7 @@ def corr(self, other=None, pairwise=None, **kwargs):
 Rolling.__doc__ = Window.__doc__
 
 
-class RollingGroupby(_GroupByMixin, Rolling):
+class RollingGroupby(WindowGroupByMixin, Rolling):
     """
     Provide a rolling groupby implementation.
     """