Singleton Per Call Context (Web Request) in Unity

A few days ago, I had an issue with ASP.Net threading. I wanted to have a singleton object per web request. I actually need this for my unit of work. I wanted to instantiate a unit of work per web request so that identity map is valid through out the request. This way I could use an IoC to inject my own IUnitOfWork to my repository classes transparently, and I could use the same instance to query and then update my entities.

ASP .NET Singleton

Just want to make sure I am not assuming something foolish here, when implementing the singleton pattern in an ASP .Net web application the static variable scope is only for the current user session, right? If a second user is accessing the site it is a different memory scope…?