diff --git a/sphinx/ext/intersphinx.py b/sphinx/ext/intersphinx.py
index f6e6d7964..95410c0c4 100644
--- a/sphinx/ext/intersphinx.py
+++ b/sphinx/ext/intersphinx.py
@@ -29,26 +29,32 @@ from typing import IO, TYPE_CHECKING, Any, cast
 from urllib.parse import urlsplit, urlunsplit
 
 from docutils import nodes
-from docutils.nodes import Element, Node, TextElement, system_message
-from docutils.utils import Reporter, relative_path
+from docutils.utils import relative_path
 
 import sphinx
 from sphinx.addnodes import pending_xref
-from sphinx.application import Sphinx
 from sphinx.builders.html import INVENTORY_FILENAME
-from sphinx.config import Config
-from sphinx.domains import Domain
-from sphinx.environment import BuildEnvironment
 from sphinx.errors import ExtensionError
 from sphinx.locale import _, __
 from sphinx.transforms.post_transforms import ReferencesResolver
 from sphinx.util import logging, requests
 from sphinx.util.docutils import CustomReSTDispatcher, SphinxRole
 from sphinx.util.inventory import InventoryFile
-from sphinx.util.typing import Inventory, InventoryItem, RoleFunction
 
 if TYPE_CHECKING:
     from types import ModuleType
+    from typing import Tuple, Union
+
+    from docutils.nodes import Node, TextElement, system_message
+    from docutils.utils import Reporter
+
+    from sphinx.application import Sphinx
+    from sphinx.config import Config
+    from sphinx.domains import Domain
+    from sphinx.environment import BuildEnvironment
+    from sphinx.util.typing import Inventory, InventoryItem, RoleFunction
+
+    InventoryCacheEntry = Tuple[Union[str, None], int, Inventory]
 
 logger = logging.getLogger(__name__)
 
@@ -60,12 +66,22 @@ class InventoryAdapter:
         self.env = env
 
         if not hasattr(env, 'intersphinx_cache'):
+            # initial storage when fetching inventories before processing
             self.env.intersphinx_cache = {}  # type: ignore
+
             self.env.intersphinx_inventory = {}  # type: ignore
             self.env.intersphinx_named_inventory = {}  # type: ignore
 
     @property
-    def cache(self) -> dict[str, tuple[str, int, Inventory]]:
+    def cache(self) -> dict[str, InventoryCacheEntry]:
+        """Intersphinx cache.
+
+        - Key is the URI of the remote inventory
+        - Element one is the key given in the Sphinx intersphinx_mapping
+          configuration value
+        - Element two is a time value for cache invalidation, a float
+        - Element three is the loaded remote inventory, type Inventory
+        """
         return self.env.intersphinx_cache  # type: ignore
 
     @property
@@ -152,7 +168,7 @@ def _get_safe_url(url: str) -> str:
         return urlunsplit(frags)
 
 
-def fetch_inventory(app: Sphinx, uri: str, inv: Any) -> Any:
+def fetch_inventory(app: Sphinx, uri: str, inv: str) -> Inventory:
     """Fetch, parse and return an intersphinx inventory file."""
     # both *uri* (base URI of the links to generate) and *inv* (actual
     # location of the inventory file) can be local or remote URIs
@@ -192,7 +208,12 @@ def fetch_inventory(app: Sphinx, uri: str, inv: Any) -> Any:
 
 
 def fetch_inventory_group(
-    name: str, uri: str, invs: Any, cache: Any, app: Any, now: float,
+    name: str | None,
+    uri: str,
+    invs: tuple[str | None, ...],
+    cache: dict[str, InventoryCacheEntry],
+    app: Sphinx,
+    now: int,
 ) -> bool:
     cache_time = now - app.config.intersphinx_cache_limit * 86400
     failures = []
@@ -211,7 +232,7 @@ def fetch_inventory_group(
                     failures.append(err.args)
                     continue
                 if invdata:
-                    cache[uri] = (name, now, invdata)
+                    cache[uri] = name, now, invdata
                     return True
         return False
     finally:
@@ -235,6 +256,9 @@ def load_mappings(app: Sphinx) -> None:
 
     with concurrent.futures.ThreadPoolExecutor() as pool:
         futures = []
+        name: str | None
+        uri: str
+        invs: tuple[str | None, ...]
         for name, (uri, invs) in app.config.intersphinx_mapping.values():
             futures.append(pool.submit(
                 fetch_inventory_group, name, uri, invs, inventories.cache, app, now,
@@ -263,7 +287,7 @@ def load_mappings(app: Sphinx) -> None:
 
 def _create_element_from_result(domain: Domain, inv_name: str | None,
                                 data: InventoryItem,
-                                node: pending_xref, contnode: TextElement) -> Element:
+                                node: pending_xref, contnode: TextElement) -> nodes.reference:
     proj, version, uri, dispname = data
     if '://' not in uri and node.get('refdoc'):
         # get correct path in case of subdirectories
@@ -295,7 +319,7 @@ def _resolve_reference_in_domain_by_target(
         inv_name: str | None, inventory: Inventory,
         domain: Domain, objtypes: list[str],
         target: str,
-        node: pending_xref, contnode: TextElement) -> Element | None:
+        node: pending_xref, contnode: TextElement) -> nodes.reference | None:
     for objtype in objtypes:
         if objtype not in inventory:
             # Continue if there's nothing of this kind in the inventory
@@ -328,7 +352,7 @@ def _resolve_reference_in_domain(env: BuildEnvironment,
                                  honor_disabled_refs: bool,
                                  domain: Domain, objtypes: list[str],
                                  node: pending_xref, contnode: TextElement,
-                                 ) -> Element | None:
+                                 ) -> nodes.reference | None:
     # we adjust the object types for backwards compatibility
     if domain.name == 'std' and 'cmdoption' in objtypes:
         # until Sphinx-1.6, cmdoptions are stored as std:option
@@ -361,7 +385,7 @@ def _resolve_reference_in_domain(env: BuildEnvironment,
 
 def _resolve_reference(env: BuildEnvironment, inv_name: str | None, inventory: Inventory,
                        honor_disabled_refs: bool,
-                       node: pending_xref, contnode: TextElement) -> Element | None:
+                       node: pending_xref, contnode: TextElement) -> nodes.reference | None:
     # disabling should only be done if no inventory is given
     honor_disabled_refs = honor_disabled_refs and inv_name is None
 
@@ -407,7 +431,7 @@ def inventory_exists(env: BuildEnvironment, inv_name: str) -> bool:
 def resolve_reference_in_inventory(env: BuildEnvironment,
                                    inv_name: str,
                                    node: pending_xref, contnode: TextElement,
-                                   ) -> Element | None:
+                                   ) -> nodes.reference | None:
     """Attempt to resolve a missing reference via intersphinx references.
 
     Resolution is tried in the given inventory with the target as is.
@@ -422,7 +446,7 @@ def resolve_reference_in_inventory(env: BuildEnvironment,
 def resolve_reference_any_inventory(env: BuildEnvironment,
                                     honor_disabled_refs: bool,
                                     node: pending_xref, contnode: TextElement,
-                                    ) -> Element | None:
+                                    ) -> nodes.reference | None:
     """Attempt to resolve a missing reference via intersphinx references.
 
     Resolution is tried with the target as is in any inventory.
@@ -434,7 +458,7 @@ def resolve_reference_any_inventory(env: BuildEnvironment,
 
 def resolve_reference_detect_inventory(env: BuildEnvironment,
                                        node: pending_xref, contnode: TextElement,
-                                       ) -> Element | None:
+                                       ) -> nodes.reference | None:
     """Attempt to resolve a missing reference via intersphinx references.
 
     Resolution is tried first with the target as is in any inventory.
@@ -462,7 +486,7 @@ def resolve_reference_detect_inventory(env: BuildEnvironment,
 
 
 def missing_reference(app: Sphinx, env: BuildEnvironment, node: pending_xref,
-                      contnode: TextElement) -> Element | None:
+                      contnode: TextElement) -> nodes.reference | None:
     """Attempt to resolve a missing reference via intersphinx references."""
 
     return resolve_reference_detect_inventory(env, node, contnode)
diff --git a/sphinx/util/inventory.py b/sphinx/util/inventory.py
index a879a17dd..123a86d25 100644
--- a/sphinx/util/inventory.py
+++ b/sphinx/util/inventory.py
@@ -7,7 +7,7 @@ import zlib
 from typing import IO, TYPE_CHECKING, Callable, Iterator
 
 from sphinx.util import logging
-from sphinx.util.typing import Inventory
+from sphinx.util.typing import Inventory, InventoryItem
 
 BUFSIZE = 16 * 1024
 logger = logging.getLogger(__name__)
@@ -133,8 +133,8 @@ class InventoryFile:
             if location.endswith('$'):
                 location = location[:-1] + name
             location = join(uri, location)
-            invdata.setdefault(type, {})[name] = (projname, version,
-                                                  location, dispname)
+            inv_item: InventoryItem = projname, version, location, dispname
+            invdata.setdefault(type, {})[name] = inv_item
         return invdata
 
     @classmethod
diff --git a/sphinx/util/typing.py b/sphinx/util/typing.py
index 3f2acb822..d4e87ef1d 100644
--- a/sphinx/util/typing.py
+++ b/sphinx/util/typing.py
@@ -51,7 +51,12 @@ OptionSpec = Dict[str, Callable[[str], Any]]
 TitleGetter = Callable[[nodes.Node], str]
 
 # inventory data on memory
-InventoryItem = Tuple[str, str, str, str]
+InventoryItem = Tuple[
+    str,  # project name
+    str,  # project version
+    str,  # URL
+    str,  # display name
+]
 Inventory = Dict[str, Dict[str, InventoryItem]]
 
 
diff --git a/tests/test_util_inventory.py b/tests/test_util_inventory.py
index e79602330..583edf669 100644
--- a/tests/test_util_inventory.py
+++ b/tests/test_util_inventory.py
@@ -4,7 +4,7 @@ import posixpath
 import zlib
 from io import BytesIO
 
-from sphinx.ext.intersphinx import InventoryFile
+from sphinx.util.inventory import InventoryFile
 
 inventory_v1 = b'''\
 # Sphinx inventory version 1