Shibboleth - from web page to REST API

The scenario is this: 1. There is a web application with a browser UI. 2. User has to log in to the Web UI. We would use Shibboleth for authentication (SSO) 3. The application connects to various backend components via REST API's 4. We are considering the REST API's are hooked with Shibboleth through the Shibboleth Service Provider

Once logged in the web app should pass the use context (session) to the REST API.

Is this scenario supported by Shibboleth? What is the best way to pass the session context to the REST API so that it validates the session through its service provider?