My understanding is currently you can self host WebAPI using Katana, and MVC will have this capability in a future version. Essentially Katana will be a hosting option available to both MVC and WebAPI.
Kestrel has entered the picture, and I see a few MS employees blogging about it demonstrating hosting ASP.NET vNext on Linux.
My understanding is that both Kestrel and Katana implement the OWIN pipeline.
From there it is all a bit fuzzy. I ask myself, why has Kestrel entered the picture, when it seems Katana could serve the same purpose if you compiled it with mono and made some efforts to make it cross platform compatible(perhaps easier said than done).
Do Kestrel and Katana serve the same purpose? Or is one specialized in some way that the other is not?
Will Kestrel eventually be a viable choice for Windows deployments? Or will it be specialized for non-Windows environments and Katana still the choice for Windows?
I recognize that I'm possibly asking for an apple to oranges comparison due to my lack of knowledge of Katana/Kestrel, but if the answer is "Oranges have more of an acidic taste than apples" then that IMO is a perfectly valid answer.
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.