diff --git a/CLAUDE.md b/CLAUDE.md
index a2c067c..499a7c3 100644
--- a/CLAUDE.md
+++ b/CLAUDE.md
@@ -499,7 +499,10 @@ image URLs come from the feed row (`Model/DataExporter/Provider/ImageUrls`).
   names, each remaining slice in the shape its reader takes, so no value is
   stored twice and no reader parses at request time (`customAttributes` the raw
   value per attribute code, an image type and a gallery entry the media file, a
-  URL rewrite the request path, `categoryData` as `categoryIds`),
+  URL rewrite the request path, `categoryData` as `categoryIds`, the category product index with
+  the anchor ancestors; `categoryAssignmentIds` (`Model/DataExporter/Provider/CategoryAssignments`)
+  holds the rows of `catalog_category_product`, which the model takes as `category_ids` because core's
+  `getCategoryIds()` reads them),
   prices = the feed rows under `prices` with their customer
   `group` id (the feed names a group by the hash of its id; the writer maps it
   back, rows of an unknown group are dropped; the feed's all-groups row comes
diff --git a/src/CatalogStorefront/Model/DataExporter/Provider/CategoryAssignments.php b/src/CatalogStorefront/Model/DataExporter/Provider/CategoryAssignments.php
new file mode 100644
index 0000000..e521c9c
--- /dev/null
+++ b/src/CatalogStorefront/Model/DataExporter/Provider/CategoryAssignments.php
@@ -0,0 +1,50 @@
+<?php
+declare(strict_types=1);
+
+namespace GraphCommerce\CatalogStorefront\Model\DataExporter\Provider;
+
+use Magento\Framework\App\ResourceConnection;
+
+/**
+ * Adds every category a product is assigned to as `categoryAssignmentIds`, the rows of
+ * catalog_category_product that core's `getCategoryIds()` reads. The feed's `categoryData` comes
+ * from the category product index, which adds the anchor ancestors and leaves out the root, so a
+ * model built from it finds a category core's model does not.
+ */
+class CategoryAssignments
+{
+    public function __construct(
+        private readonly ResourceConnection $resourceConnection,
+    ) {
+    }
+
+    public function get(array $values): array
+    {
+        $ids = array_unique(array_map(static fn(array $value) => (int)$value['productId'], $values));
+        if (!$ids) {
+            return [];
+        }
+        $connection = $this->resourceConnection->getConnection();
+        $categories = [];
+        $select = $connection->select()
+            ->from($this->resourceConnection->getTableName('catalog_category_product'), ['product_id', 'category_id'])
+            ->where('product_id IN (?)', $ids)
+            ->order('category_id');
+        foreach ($connection->fetchAll($select) as $row) {
+            $categories[(int)$row['product_id']][] = (int)$row['category_id'];
+        }
+
+        $output = [];
+        foreach ($values as $value) {
+            foreach ($categories[(int)$value['productId']] ?? [] as $categoryId) {
+                $output[$value['storeViewCode'] . '_' . $value['productId'] . '_' . $categoryId] = [
+                    'productId' => $value['productId'],
+                    'storeViewCode' => $value['storeViewCode'],
+                    'categoryAssignmentIds' => $categoryId,
+                ];
+            }
+        }
+
+        return $output;
+    }
+}
diff --git a/src/CatalogStorefront/Model/Read/ProductModelBuilder.php b/src/CatalogStorefront/Model/Read/ProductModelBuilder.php
index 0462628..446cb65 100644
--- a/src/CatalogStorefront/Model/Read/ProductModelBuilder.php
+++ b/src/CatalogStorefront/Model/Read/ProductModelBuilder.php
@@ -98,8 +98,11 @@ public function build(array $document, int $storeId): ?Product
             $data['price'] = $fallbackRow['regular'];
         }
 
-        if (!empty($document['categoryIds'])) {
-            $data['category_ids'] = array_map('strval', $document['categoryIds']);
+        // Core's getCategoryIds() reads the assignments. `categoryIds` holds the category product
+        // index, which adds the anchor ancestors: the current category of a page then applies to
+        // the model where it does not apply to core's, and the product URL takes the category path.
+        if (!empty($document['categoryAssignmentIds'])) {
+            $data['category_ids'] = array_map('strval', $document['categoryAssignmentIds']);
         }
 
         foreach ((array)($document['customAttributes'] ?? []) as $code => $value) {
diff --git a/src/CatalogStorefront/Test/Unit/Model/DataExporter/Provider/CategoryAssignmentsTest.php b/src/CatalogStorefront/Test/Unit/Model/DataExporter/Provider/CategoryAssignmentsTest.php
new file mode 100644
index 0000000..9e291a2
--- /dev/null
+++ b/src/CatalogStorefront/Test/Unit/Model/DataExporter/Provider/CategoryAssignmentsTest.php
@@ -0,0 +1,62 @@
+<?php
+declare(strict_types=1);
+
+namespace GraphCommerce\CatalogStorefront\Test\Unit\Model\DataExporter\Provider;
+
+use GraphCommerce\CatalogStorefront\Model\DataExporter\Provider\CategoryAssignments;
+use Magento\Framework\App\ResourceConnection;
+use Magento\Framework\DB\Adapter\AdapterInterface;
+use Magento\Framework\DB\Select;
+use PHPUnit\Framework\TestCase;
+
+class CategoryAssignmentsTest extends TestCase
+{
+    public function testEveryAssignmentIsOneRowPerProductAndStoreViewInCategoryIdOrder(): void
+    {
+        // The root (2) is an assignment as well, as core's getCategoryIds() returns it.
+        $provider = $this->provider([
+            ['product_id' => '1812', 'category_id' => '2'],
+            ['product_id' => '1812', 'category_id' => '30'],
+            ['product_id' => '6', 'category_id' => '4'],
+        ]);
+
+        $output = $provider->get([
+            ['productId' => '1812', 'storeViewCode' => 'default'],
+            ['productId' => '6', 'storeViewCode' => 'default'],
+            ['productId' => '7', 'storeViewCode' => 'default'],
+            ['productId' => '1812', 'storeViewCode' => 'second'],
+        ]);
+
+        self::assertSame([
+            'default_1812_2' => ['productId' => '1812', 'storeViewCode' => 'default', 'categoryAssignmentIds' => 2],
+            'default_1812_30' => ['productId' => '1812', 'storeViewCode' => 'default', 'categoryAssignmentIds' => 30],
+            'default_6_4' => ['productId' => '6', 'storeViewCode' => 'default', 'categoryAssignmentIds' => 4],
+            'second_1812_2' => ['productId' => '1812', 'storeViewCode' => 'second', 'categoryAssignmentIds' => 2],
+            'second_1812_30' => ['productId' => '1812', 'storeViewCode' => 'second', 'categoryAssignmentIds' => 30],
+        ], $output);
+    }
+
+    public function testNoProductsMeansNoQuery(): void
+    {
+        $resource = $this->createMock(ResourceConnection::class);
+        $resource->expects(self::never())->method('getConnection');
+
+        self::assertSame([], (new CategoryAssignments($resource))->get([]));
+    }
+
+    private function provider(array $rows): CategoryAssignments
+    {
+        $select = $this->createMock(Select::class);
+        $select->method('from')->willReturnSelf();
+        $select->method('where')->willReturnSelf();
+        $select->method('order')->willReturnSelf();
+        $connection = $this->createMock(AdapterInterface::class);
+        $connection->method('select')->willReturn($select);
+        $connection->method('fetchAll')->willReturn($rows);
+        $resource = $this->createMock(ResourceConnection::class);
+        $resource->method('getConnection')->willReturn($connection);
+        $resource->method('getTableName')->willReturnArgument(0);
+
+        return new CategoryAssignments($resource);
+    }
+}
diff --git a/src/CatalogStorefront/Test/Unit/Model/Read/ProductModelBuilderTest.php b/src/CatalogStorefront/Test/Unit/Model/Read/ProductModelBuilderTest.php
index 4637d10..7fd4a8c 100644
--- a/src/CatalogStorefront/Test/Unit/Model/Read/ProductModelBuilderTest.php
+++ b/src/CatalogStorefront/Test/Unit/Model/Read/ProductModelBuilderTest.php
@@ -118,11 +118,12 @@ public function testAFixedBundleIsBuiltAsABundle(): void
         $this->assertSame('1', $this->data['price_type']);
     }
 
-    public function testCategoryIdsAreTheDocumentsCategoryIdsAsStrings(): void
+    public function testCategoryIdsAreTheAssignmentsAsStringsNotTheIndex(): void
     {
-        $this->build(['categoryIds' => [24, 25]]);
+        // The index adds the anchor ancestors 24 and 25 and leaves out the root 2.
+        $this->build(['categoryIds' => [24, 25, 30, 34], 'categoryAssignmentIds' => [2, 30, 34]]);
 
-        $this->assertSame(['24', '25'], $this->data['category_ids']);
+        $this->assertSame(['2', '30', '34'], $this->data['category_ids']);
     }
 
     public function testAnAttributeValueComesFromTheCustomAttributeMap(): void
diff --git a/src/CatalogStorefront/etc/et_schema.xml b/src/CatalogStorefront/etc/et_schema.xml
index 0fffc89..1e29044 100644
--- a/src/CatalogStorefront/etc/et_schema.xml
+++ b/src/CatalogStorefront/etc/et_schema.xml
@@ -29,6 +29,10 @@
             <using field="productId"/>
             <using field="storeViewCode"/>
         </field>
+        <field name="categoryAssignmentIds" type="Int" repeated="true" provider="GraphCommerce\CatalogStorefront\Model\DataExporter\Provider\CategoryAssignments">
+            <using field="productId"/>
+            <using field="storeViewCode"/>
+        </field>
         <field name="taxClassId" type="Int" provider="GraphCommerce\CatalogStorefront\Model\DataExporter\Provider\TaxClass">
             <using field="productId"/>
             <using field="storeViewCode"/>