diff --git a/sphinx/addnodes.py b/sphinx/addnodes.py
index 5d26643ed..a2fb776e4 100644
--- a/sphinx/addnodes.py
+++ b/sphinx/addnodes.py
@@ -119,13 +119,13 @@ class toctree(nodes.General, nodes.Element, translatable):
 # Domain-specific object descriptions (class, function etc.)
 #############################################################
 
-class _desc_classes_injector(nodes.TextElement):
+class _desc_classes_injector(nodes.Element):
     """Helper base class for injecting a fixes list of classes.
 
     Use as the first base class.
     """
 
-    classes = []  # type: List[str]
+    classes: List[str] = []
 
     def __init__(self, *args: Any, **kwargs: Any) -> None:
         super().__init__(*args, **kwargs)
diff --git a/sphinx/transforms/post_transforms/__init__.py b/sphinx/transforms/post_transforms/__init__.py
index bcc9caf00..e2899d994 100644
--- a/sphinx/transforms/post_transforms/__init__.py
+++ b/sphinx/transforms/post_transforms/__init__.py
@@ -233,7 +233,7 @@ class SigElementFallbackTransform(SphinxPostTransform):
             node.replace_self(newnode)
 
 
-class DescSigAddDomainAsClass(SphinxPostTransform):
+class PropagateDescDomain(SphinxPostTransform):
     """Add the domain name of the parent node as a class in each desc_signature node."""
     default_priority = 200
 
@@ -246,7 +246,7 @@ def setup(app: Sphinx) -> Dict[str, Any]:
     app.add_post_transform(ReferencesResolver)
     app.add_post_transform(OnlyNodeTransform)
     app.add_post_transform(SigElementFallbackTransform)
-    app.add_post_transform(DescSigAddDomainAsClass)
+    app.add_post_transform(PropagateDescDomain)
 
     return {
         'version': 'builtin',