diff --git a/python_modules/dagster/dagster/_core/definitions/asset_selection.py b/python_modules/dagster/dagster/_core/definitions/asset_selection.py
index 71209031ee0d1..264a2ec3883bd 100644
--- a/python_modules/dagster/dagster/_core/definitions/asset_selection.py
+++ b/python_modules/dagster/dagster/_core/definitions/asset_selection.py
@@ -18,7 +18,7 @@
 )
 
 from .asset_check_spec import AssetCheckHandle
-from .asset_graph import AssetGraph
+from .asset_graph import AssetGraph, InternalAssetGraph
 from .assets import AssetsDefinition
 from .events import (
     AssetKey,
@@ -256,7 +256,7 @@ def upstream_source_assets(self) -> "SourceAssetSelection":
 
     @public
     @staticmethod
-    def asset_checks_for_assets(*assets_defs: AssetsDefinition) -> "KeysAssetSelection":
+    def asset_checks_for_assets(*assets_defs: AssetsDefinition) -> "AssetChecksForAssetKeys":
         """Returns a selection with the asset checks that target the provided assets."""
         return AssetChecksForAssetKeys(
             [key for assets_def in assets_defs for key in assets_def.keys]
@@ -309,11 +309,15 @@ def resolve(
     def resolve_inner(self, asset_graph: AssetGraph) -> AbstractSet[AssetKey]:
         raise NotImplementedError()
 
-    def resolve_checks(self, asset_graph: AssetGraph) -> AbstractSet[AssetCheckHandle]:
-        """We don't need this method currently, but it makes things consistent with resolve_inner."""
+    def resolve_checks(self, asset_graph: InternalAssetGraph) -> AbstractSet[AssetCheckHandle]:
+        """We don't need this method currently, but it makes things consistent with resolve_inner. Currently
+        we don't store checks in the ExternalAssetGraph, so we only support InternalAssetGraph.
+        """
         return self.resolve_checks_inner(asset_graph)
 
-    def resolve_checks_inner(self, asset_graph: AssetGraph) -> AbstractSet[AssetCheckHandle]:
+    def resolve_checks_inner(
+        self, asset_graph: InternalAssetGraph
+    ) -> AbstractSet[AssetCheckHandle]:
         """By default, resolve to checks that target the selected assets. This is overriden for particular selections."""
         asset_keys = self.resolve(asset_graph)
         return {
@@ -380,12 +384,13 @@ def resolve_inner(self, asset_graph: AssetGraph) -> AbstractSet[AssetKey]:
         return asset_graph.materializable_asset_keys
 
 
-
 class AllAssetCheckSelection(AssetSelection):
     def resolve_inner(self, asset_graph: AssetGraph) -> AbstractSet[AssetKey]:
         return set()
 
-    def resolve_checks_inner(self, asset_graph: AssetGraph) -> AbstractSet[AssetCheckHandle]:
+    def resolve_checks_inner(
+        self, asset_graph: InternalAssetGraph
+    ) -> AbstractSet[AssetCheckHandle]:
         return asset_graph.asset_check_handles
 
 
@@ -396,7 +401,9 @@ def __init__(self, keys: Sequence[AssetKey]):
     def resolve_inner(self, asset_graph: AssetGraph) -> AbstractSet[AssetKey]:
         return set()
 
-    def resolve_checks_inner(self, asset_graph: AssetGraph) -> AbstractSet[AssetCheckHandle]:
+    def resolve_checks_inner(
+        self, asset_graph: InternalAssetGraph
+    ) -> AbstractSet[AssetCheckHandle]:
         return {
             handle for handle in asset_graph.asset_check_handles if handle.asset_key in self._keys
         }
@@ -409,7 +416,9 @@ def __init__(self, asset_check_handles: Sequence[AssetCheckHandle]):
     def resolve_inner(self, asset_graph: AssetGraph) -> AbstractSet[AssetKey]:
         return set()
 
-    def resolve_checks_inner(self, asset_graph: AssetGraph) -> AbstractSet[AssetCheckHandle]:
+    def resolve_checks_inner(
+        self, asset_graph: InternalAssetGraph
+    ) -> AbstractSet[AssetCheckHandle]:
         return {
             handle
             for handle in asset_graph.asset_check_handles
@@ -425,7 +434,7 @@ def __init__(self, left: AssetSelection, right: AssetSelection):
     def resolve_inner(self, asset_graph: AssetGraph) -> AbstractSet[AssetKey]:
         return self._left.resolve_inner(asset_graph) & self._right.resolve_inner(asset_graph)
 
-    def resolve_checks_inner(self, asset_graph: AssetGraph) -> AbstractSet[AssetCheckHandle]:
+    def resolve_checks_inner(self, asset_graph: InternalAssetGraph) -> AbstractSet[AssetCheckHandle]:
         return self._left.resolve_checks_inner(asset_graph) & self._right.resolve_checks_inner(
             asset_graph
         )
@@ -439,7 +448,7 @@ def __init__(self, left: AssetSelection, right: AssetSelection):
     def resolve_inner(self, asset_graph: AssetGraph) -> AbstractSet[AssetKey]:
         return self._left.resolve_inner(asset_graph) - self._right.resolve_inner(asset_graph)
 
-    def resolve_checks_inner(self, asset_graph: AssetGraph) -> AbstractSet[AssetCheckHandle]:
+    def resolve_checks_inner(self, asset_graph: InternalAssetGraph) -> AbstractSet[AssetCheckHandle]:
         return self._left.resolve_checks_inner(asset_graph) - self._right.resolve_checks_inner(
             asset_graph
         )
@@ -565,7 +574,7 @@ def __init__(self, left: AssetSelection, right: AssetSelection):
     def resolve_inner(self, asset_graph: AssetGraph) -> AbstractSet[AssetKey]:
         return self._left.resolve_inner(asset_graph) | self._right.resolve_inner(asset_graph)
 
-    def resolve_checks_inner(self, asset_graph: AssetGraph) -> AbstractSet[AssetCheckHandle]:
+    def resolve_checks_inner(self, asset_graph: InternalAssetGraph) -> AbstractSet[AssetCheckHandle]:
         return self._left.resolve_checks_inner(asset_graph) | self._right.resolve_checks_inner(
             asset_graph
         )
diff --git a/python_modules/dagster/dagster/_core/definitions/external_asset_graph.py b/python_modules/dagster/dagster/_core/definitions/external_asset_graph.py
index e50ca007e508b..b112b466158db 100644
--- a/python_modules/dagster/dagster/_core/definitions/external_asset_graph.py
+++ b/python_modules/dagster/dagster/_core/definitions/external_asset_graph.py
@@ -13,6 +13,7 @@
 )
 
 import dagster._check as check
+from dagster._core.definitions.asset_check_spec import AssetCheckHandle
 from dagster._core.definitions.assets_job import ASSET_BASE_JOB_PREFIX
 from dagster._core.definitions.auto_materialize_policy import AutoMaterializePolicy
 from dagster._core.host_representation.external import ExternalRepository
@@ -300,3 +301,7 @@ def split_asset_keys_by_repository(
                 asset_key
             )
         return list(asset_keys_by_repo.values())
+
+    @property
+    def asset_check_handles(self) -> AbstractSet[AssetCheckHandle]:
+        raise NotImplementedError("ExternalAssetGraph does not support asset checks")