BUG: min/max on empty categorical fails

doc/source/whatsnew/v1.0.0.rst

@@ -667,6 +667,7 @@ Categorical
   same type as if one used the :meth:`.str.` / :meth:`.dt.` on a :class:`Series` of that type. E.g. when accessing :meth:`Series.dt.tz_localize` on a
   :class:`Categorical` with duplicate entries, the accessor was skipping duplicates (:issue:`27952`)
 - Bug in :meth:`DataFrame.replace` and :meth:`Series.replace` that would give incorrect results on categorical data (:issue:`26988`)
+- Bug where calling :meth:`Categorical.min` or :meth:`Categorical.max` on an empty Categorical would raise a numpy exception.
 
 
 Datetimelike

pandas/core/arrays/categorical.py

@@ -2126,6 +2126,10 @@ def min(self, skipna=True):
         min : the minimum of this `Categorical`
         """
         self.check_for_ordered("min")
+
+        if len(self._codes) == 0:
+            return np.nan
+
         good = self._codes != -1
         if not good.all():
             if skipna:
@@ -2153,6 +2157,10 @@ def max(self, skipna=True):
         max : the maximum of this `Categorical`
         """
         self.check_for_ordered("max")
+
+        if len(self._codes) == 0:
+            return np.nan
+
         good = self._codes != -1
         if not good.all():
             if skipna:

pandas/tests/reductions/test_reductions.py

@@ -1060,6 +1060,12 @@ def test_min_max_skipna(self, skipna):
             assert np.isnan(_min)
             assert np.isnan(_max)
 
+    def test_min_max_empty(self):
+        cat = Series(Categorical([], categories=list("ABC"), ordered=True))
+
+        assert isna(cat.min())
+        assert isna(cat.max())
+
 
 class TestSeriesMode:
     # Note: the name TestSeriesMode indicates these tests