diff --git a/dvc/data/db/index.py b/dvc/data/db/index.py
index 60c095c8cd..21bb3b12fb 100644
--- a/dvc/data/db/index.py
+++ b/dvc/data/db/index.py
@@ -95,9 +95,7 @@ def __init__(
         self.index_dir = os.path.join(tmp_dir, self.INDEX_DIR, name)
         makedirs(self.index_dir, exist_ok=True)
         self.fs = LocalFileSystem()
-        cache = Cache(
-            self.index_dir, eviction_policy="none", disk_type="index"
-        )
+        cache = Cache(self.index_dir, eviction_policy="none", type="index")
         self.index = Index.fromcache(cache)
 
     def __iter__(self):
diff --git a/dvc/objects/cache.py b/dvc/objects/cache.py
index 0aa92d2c47..5f61535ca8 100644
--- a/dvc/objects/cache.py
+++ b/dvc/objects/cache.py
@@ -35,9 +35,8 @@ def wrapped(self, *args, **kwargs):
 class Disk(disk):
     """Reraise pickle-related errors as DiskError."""
 
-    def __init__(self, *args, type=None, **kwargs):
-        super().__init__(*args, **kwargs)
-        self._type = type or os.path.basename(self._directory)
+    # we need type to differentiate cache for better error messages
+    _type: str
 
     put = translate_pickle_error(disk.put)
     get = translate_pickle_error(disk.get)
@@ -53,9 +52,14 @@ def __init__(
         directory: str = None,
         timeout: int = 60,
         disk: disk = Disk,  # pylint: disable=redefined-outer-name
+        type: str = None,
         **settings: Any,
     ) -> None:
         settings.setdefault("disk_pickle_protocol", 4)
         super().__init__(
             directory=directory, timeout=timeout, disk=disk, **settings
         )
+        self.disk._type = self._type = type or os.path.basename(self.directory)
+
+    def __getstate__(self):
+        return (*super().__getstate__(), self._type)
diff --git a/tests/unit/objects/test_cache.py b/tests/unit/objects/test_cache.py
index 39d59d65c5..5bcb0bd7cc 100644
--- a/tests/unit/objects/test_cache.py
+++ b/tests/unit/objects/test_cache.py
@@ -17,7 +17,7 @@ def test_pickle_protocol_error(tmp_dir, disk_type):
     cache = Cache(
         directory,
         disk_pickle_protocol=pickle.HIGHEST_PROTOCOL + 1,
-        disk_type=disk_type,
+        type=disk_type,
     )
     with pytest.raises(DiskError) as exc, cache as cache:
         set_value(cache, "key", ("value1", "value2"))