Unit Testing the IoC container itself

I don't think this was asked before, although it's really hard to search for a term like unit test ioc container and not find a question about how to implement IoC in order to perform unit tests.

I would like to have unit tests against the IoC container itself basically because sometimes I have issues with the container (like you could with any other part of an application), and it's pretty troublesome to test the resolution of dependencies merely debugging.

If I could introduce unit tests for these cases, I think it would save me a lot of trouble.

Update

Is something like this, not an Unit Test? Is it an integration test?

[TestClass]
 public class IoC
 {
     private IWindsorContainer _container;
 
     [TestInitialize]
     public void TestInit()
     {
         _container = new WindsorContainer();
         _container.Install(new WindsorInstaller());
     }
 
     [TestMethod]
     public void ContainerShouldResolve_MembershipProvider()
     {
         ContainerShouldResolve<IMembershipProvider>();
     }
 
     public void ContainerShouldResolve<T>()
     {
         T result = _container.Resolve<T>();
         Assert.IsInstanceOfType(result, typeof(T));
     }
 }
 

The only real "not self-contained" reference is a connection string I had to wire into app.config. Also: when trying to resolve PerWebRequest lifestyle components I had to add the related httpModule, too.

By the way: by doing this I found out the source of my issue in little time compared to what it was taking me to debug it through using the web application.

---