diff --git a/xarray/core/groupby.py b/xarray/core/groupby.py
index f038911ddbe..0425da2ffc7 100644
--- a/xarray/core/groupby.py
+++ b/xarray/core/groupby.py
@@ -44,6 +44,7 @@
     from xarray.core.utils import Frozen
 
     GroupKey = Any
+    GroupIndex = int | slice | list[int]
 
     T_GroupIndicesListInt = list[list[int]]
     T_GroupIndices = Union[T_GroupIndicesListInt, list[slice], np.ndarray]
@@ -129,11 +130,11 @@ def _dummy_copy(xarray_obj):
     return res
 
 
-def _is_one_or_none(obj):
+def _is_one_or_none(obj) -> bool:
     return obj == 1 or obj is None
 
 
-def _consolidate_slices(slices):
+def _consolidate_slices(slices: list[slice]) -> list[slice]:
     """Consolidate adjacent slices in a list of slices."""
     result = []
     last_slice = slice(None)
@@ -191,7 +192,6 @@ def __init__(self, obj: T_Xarray, name: Hashable, coords) -> None:
         self.name = name
         self.coords = coords
         self.size = obj.sizes[name]
-        self.dataarray = obj[name]
 
     @property
     def dims(self) -> tuple[Hashable]:
@@ -228,6 +228,13 @@ def __getitem__(self, key):
     def copy(self, deep: bool = True, data: Any = None):
         raise NotImplementedError
 
+    def as_dataarray(self) -> DataArray:
+        from xarray.core.dataarray import DataArray
+
+        return DataArray(
+            data=self.data, dims=(self.name,), coords=self.coords, name=self.name
+        )
+
 
 T_Group = TypeVar("T_Group", bound=Union["DataArray", "IndexVariable", _DummyGroup])
 
@@ -294,14 +301,16 @@ def _apply_loffset(
 
 
 class Grouper:
-    def __init__(self, group: T_Group):
-        self.group : T_Group | None = group
-        self.codes : np.ndarry | None = None
+    def __init__(self, group: T_Group | Hashable):
+        self.group: T_Group | Hashable = group
+
         self.labels = None
-        self.group_indices : list[list[int, ...]] | None= None
-        self.unique_coord = None
-        self.full_index : pd.Index | None = None
-        self._group_as_index = None
+        self._group_as_index: pd.Index | None = None
+
+        self.codes: DataArray
+        self.group_indices: list[int] | list[slice] | list[list[int]]
+        self.unique_coord: IndexVariable | _DummyGroup
+        self.full_index: pd.Index
 
     @property
     def name(self) -> Hashable:
@@ -334,10 +343,9 @@ def group_as_index(self) -> pd.Index:
             self._group_as_index = safe_cast_to_index(self.group1d)
         return self._group_as_index
 
-    def _resolve_group(self, obj: T_DataArray | T_Dataset) -> None:
+    def _resolve_group(self, obj: T_Xarray):
         from xarray.core.dataarray import DataArray
 
-        group: T_Group
         group = self.group
         if not isinstance(group, (DataArray, IndexVariable)):
             if not hashable(group):
@@ -346,15 +354,14 @@ def _resolve_group(self, obj: T_DataArray | T_Dataset) -> None:
                     "name of an xarray variable or dimension. "
                     f"Received {group!r} instead."
                 )
-            group_da : T_DataArray = obj[group]
-            if len(group_da) == 0:
-                raise ValueError(f"{group_da.name} must not be empty")
-
-            if group_da.name not in obj.coords and group_da.name in obj.dims:
+            group = obj[group]
+            if len(group) == 0:
+                raise ValueError(f"{group.name} must not be empty")
+            if group.name not in obj._indexes and group.name in obj.dims:
                 # DummyGroups should not appear on groupby results
                 group = _DummyGroup(obj, group.name, group.coords)
 
-        if getattr(group, "name", None) is None:
+        elif getattr(group, "name", None) is None:
             group.name = "group"
 
         self.group = group
@@ -408,10 +415,10 @@ def _factorize_dummy(self, squeeze) -> None:
             # equivalent to: group_indices = group_indices.reshape(-1, 1)
             self.group_indices = [slice(i, i + 1) for i in range(size)]
         else:
-            self.group_indices = np.arange(size)
+            self.group_indices = list(range(size))
         codes = np.arange(size)
         if isinstance(self.group, _DummyGroup):
-            self.codes = self.group.dataarray.copy(data=codes)
+            self.codes = self.group.as_dataarray().copy(data=codes)
         else:
             self.codes = self.group.copy(data=codes)
         self.unique_coord = self.group
@@ -489,7 +496,7 @@ def __init__(
             raise ValueError("index must be monotonic for resampling")
 
         if isinstance(group_as_index, CFTimeIndex):
-            self.grouper = CFTimeGrouper(
+            grouper = CFTimeGrouper(
                 freq=self.freq,
                 closed=self.closed,
                 label=self.label,
@@ -498,15 +505,16 @@ def __init__(
                 loffset=self.loffset,
             )
         else:
-            self.grouper = pd.Grouper(
+            grouper = pd.Grouper(
                 freq=self.freq,
                 closed=self.closed,
                 label=self.label,
                 origin=self.origin,
                 offset=self.offset,
             )
+        self.grouper: CFTimeGrouper | pd.Grouper = grouper
 
-    def _get_index_and_items(self):
+    def _get_index_and_items(self) -> tuple[pd.Index, pd.Series, np.ndarray]:
         first_items, codes = self.first_items()
         full_index = first_items.index
         if first_items.isnull().any():
@@ -515,7 +523,7 @@ def _get_index_and_items(self):
         full_index = full_index.rename("__resample_dim__")
         return full_index, first_items, codes
 
-    def first_items(self):
+    def first_items(self) -> tuple[pd.Series, np.ndarray]:
         from xarray import CFTimeIndex
 
         if isinstance(self.group_as_index, CFTimeIndex):
@@ -670,7 +678,7 @@ def reduce(
         raise NotImplementedError()
 
     @property
-    def groups(self) -> dict[GroupKey, slice | int | list[int]]:
+    def groups(self) -> dict[GroupKey, GroupIndex]:
         """
         Mapping from group labels to indices. The indices can be used to index the underlying object.
         """
@@ -735,7 +743,7 @@ def _binary_op(self, other, f, reflexive=False):
         dims = group.dims
 
         if isinstance(group, _DummyGroup):
-            group = coord = group.dataarray
+            group = coord = group.as_dataarray()
         else:
             coord = grouper.unique_coord
             if not isinstance(coord, DataArray):