rewrite intro to materialize

pages/authzed/concepts/authzed-materialize.mdx

@@ -1,45 +1,42 @@
 import { Callout } from 'nextra/components'
 
-# AuthZed Materialize (Early Access)
-
-AuthZed Materialize works with AuthZed Dedicated and is inspired by the Leopard index component described in the [Zanzibar paper](https://zanzibar.tech/2IoYDUFMAE:0:T).
-Much like the concept of a materialized view in relational databases, AuthZed Materialize supports SpiceDB permissions systems by precomputing permissions defined in your schema.
-
-By creating a materialized view of your permissions in a relational database, you can efficiently sort, search, and filter massive lists of authorized objects while leveraging the authorization computation capabilities of SpiceDB.
+# AuthZed Materialize
 
 <Callout type="info">
   AuthZed Materialize is available to users of AuthZed [Dedicated] as part of an early access program.
   Don't hesitate to get in touch with your AuthZed account team if you would like to participate.
 </Callout>
 
-[Dedicated]: ../guides/picking-a-product#dedicated
-
-## What Is AuthZed Materialize?
+AuthZed Materialize is inspired by the Leopard index component described in the [Zanzibar paper](https://zanzibar.tech/2IoYDUFMAE:0:T).
+Much like the concept of a materialized view in relational databases, AuthZed Materialize is a service that computes how permissions change after relationships
+are written, when those relationships affect a subject's membership in a permission set or a set’s permission on a specific resource.
+These permissions are then streamed to your client, so that you can store them as a denormalized table, and then do operations like searching, sorting, and filtering much more efficiently.
 
-Materialize streams computed permission updates to a client.
-Updates occur after a relationship is written that affects a subject's membership in a permission set or a set’s permission on a specific resource.
-The intent is for users to process these updates and store them to form a precomputed and denormalized view of SpiceDB permissions.
+AuthZed Materialize allows you to:
 
-## When To Use AuthZed Materialize?
+- speed up `CheckPermission` and `CheckBulkPermissions`
+- speed up `LookupResources` and `LookupSubjects`, especially when there is a large number of resources
+- build authorization-aware UIs, e.g. by providing a filtered and/or sorted list of more than several thousand authorized objects
+- perform ACL filtering in other secondary indexes, like a search index (e.g. ElasticSearch)
 
-If you need to provide a filtered and/or sorted list of more than several thousand authorized objects or if you need an authorization-aware search index, you probably need Materialize.
-
-The primary use case for Materialize is to denormalize computed permissions into systems that excel at data retrieval operations like searching, sorting, and filtering.
+[Dedicated]: ../guides/picking-a-product#dedicated
 
-There are some authorized object listing scenarios where [LookupResources] or [LookupSubjects], without Materialize, can return a response without a large computational cost.
-Those scenarios include:
+## Limitations
 
-1. Paginating through a list of authorized objects without sorting or filtering ([LookupResources] supports cursor-based pagination, but the list of objects is returned in a non-deterministic order)  
-2. Listing a small set (in the realm of thousands) of ordered or filtered objects.
+If there are:
 
-If you do make a [LookupResources] or [LookupSubjects] request with a significant computational cost, you can expect the request to be slow and to use a large number of system resources, leading to slower response times for other queries.
+- [Caveats]
+- [Wildcard] subject types
+- [.all]
 
-## Current Limitations
+on the path of permissions computed by Materialize, it will error out.
+However, your schema can still include them.
 
-- [Caveats](https://authzed.com/docs/spicedb/concepts/caveats) are not supported on the path of permissions computed by Materialize
-- [Wildcard](https://authzed.com/docs/spicedb/concepts/schema\#wildcards) subject types are not supported on the path of permissions computed by Materialize
+[Caveats]: https://authzed.com/docs/spicedb/concepts/caveats
+[Wildcard]: https://authzed.com/docs/spicedb/concepts/schema\#wildcards
+[.all]: https://authzed.com/docs/spicedb/concepts/schema\#all-intersection-arrow
 
-You can still use both Caveats and Wildcards, so long they are not part of the path to the permissions you've asked Materialize to query.
+[Dedicated]: ../guides/picking-a-product#dedicated
 
 ## Client SDK