diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index 0cb46a5164674..25bd3b43be3ed 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -186,6 +186,8 @@ Categorical
 - Bug in ``CategoricalIndex.reindex`` failed when ``Index`` passed with elements all in category (:issue:`28690`)
 - Bug where constructing a :class:`Categorical` from an object-dtype array of ``date`` objects did not round-trip correctly with ``astype`` (:issue:`38552`)
 - Bug in constructing a :class:`DataFrame` from an ``ndarray`` and a :class:`CategoricalDtype` (:issue:`38857`)
+- Bug in :meth:`DataFrame.reindex` was throwing ``IndexError`` when new index contained duplicates and old index was :class:`CategoricalIndex` (:issue:`38906`)
+- Bug in setting categorical values into an object-dtype column in a :class:`DataFrame` (:issue:`39136`)
 - Bug in :meth:`DataFrame.reindex` was raising ``IndexError`` when new index contained duplicates and old index was :class:`CategoricalIndex` (:issue:`38906`)
 
 Datetimelike
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index 0216334a4c0aa..6f6f17171537f 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -959,7 +959,13 @@ def setitem(self, indexer, value):
             # GH25495 - If the current dtype is not categorical,
             # we need to create a new categorical block
             values[indexer] = value
-            return self.make_block(Categorical(self.values, dtype=arr_value.dtype))
+            if values.ndim == 2:
+                # TODO(EA2D): special case not needed with 2D EAs
+                if values.shape[-1] != 1:
+                    # shouldn't get here (at least until 2D EAs)
+                    raise NotImplementedError
+                values = values[:, 0]
+            return self.make_block(Categorical(values, dtype=arr_value.dtype))
 
         elif exact_match and is_ea_value:
             # GH#32395 if we're going to replace the values entirely, just
diff --git a/pandas/tests/indexing/test_iloc.py b/pandas/tests/indexing/test_iloc.py
index 7dcb30efb8184..1668123e782ff 100644
--- a/pandas/tests/indexing/test_iloc.py
+++ b/pandas/tests/indexing/test_iloc.py
@@ -65,6 +65,50 @@ def test_iloc_getitem_list_int(self):
 class TestiLocBaseIndependent:
     """Tests Independent Of Base Class"""
 
+    @pytest.mark.parametrize(
+        "key",
+        [
+            slice(None),
+            slice(3),
+            range(3),
+            [0, 1, 2],
+            Index(range(3)),
+            np.asarray([0, 1, 2]),
+        ],
+    )
+    @pytest.mark.parametrize("indexer", [tm.loc, tm.iloc])
+    def test_iloc_setitem_fullcol_categorical(self, indexer, key):
+        frame = DataFrame({0: range(3)}, dtype=object)
+
+        cat = Categorical(["alpha", "beta", "gamma"])
+        expected = DataFrame({0: cat})
+        # NB: pending GH#38896, the expected likely should become
+        #  expected= DataFrame({"A": cat.astype(object)})
+        # and should remain a view on the original values
+
+        assert frame._mgr.blocks[0]._can_hold_element(cat)
+
+        df = frame.copy()
+        orig_vals = df.values
+        indexer(df)[key, 0] = cat
+
+        overwrite = not isinstance(key, slice)
+
+        tm.assert_frame_equal(df, expected)
+
+        # TODO: this inconsistency is likely undesired GH#39986
+        if overwrite:
+            # check that we overwrote underlying
+            tm.assert_numpy_array_equal(orig_vals, df.values)
+
+        # but we don't have a view on orig_vals
+        orig_vals[0, 0] = 19
+        assert df.iloc[0, 0] != 19
+
+        # check we dont have a view on cat (may be undesired GH#39986)
+        df.iloc[0, 0] = "gamma"
+        assert cat[0] != "gamma"
+
     @pytest.mark.parametrize("box", [pd_array, Series])
     def test_iloc_setitem_ea_inplace(self, frame_or_series, box):
         # GH#38952 Case with not setting a full column