Katana is Microsoft’s OWIN implementation and also includes some middleware components for security/authentication, serving static files, and a few other things.
Kestrel is Microsoft’s cross-platform development web server that can be used with ASP.NET 5.
ASP.NET 5 does not implement OWIN, but has a “bridge” to enable OWIN components to be used in ASP.NET 5 applications, including running on Kestrel.