Startup.cs

using AppFunc = Func<IDictionary<string, object>, Task>;

using AddMiddleware = Action<Func<
    Func<IDictionary<string, object>, Task>,
    Func<IDictionary<string, object>, Task>
    >>;

public class Startup
{
    public void Configure(IApplicationBuilder app)
    {
        var oAuthOptions = new OAuthAuthorizationServerOptions
        {
            TokenEndpointPath = new PathString("/token"),
            AuthorizeEndpointPath = new PathString("/external-login"),
        };

        var twitterOptions = new TwitterAuthenticationOptions
        {
            ConsumerKey = "lKtgWiK8KSvnP6QF45Zeq2rJm",
            ConsumerSecret = "EYbUk9pqhtsIzUA82hSgjqxwXDt2KFGZVaaNeCggHUj7oVHUEI",
            AuthenticationMode = AuthenticationMode.Active
        };

        app.UseOwin(owin =>
        {
            owin.UseKatana(katana =>
            {
                katana.UseCookieAuthentication(new CookieAuthenticationOptions());
                katana.UseExternalSignInCookie(DefaultAuthenticationTypes.ExternalCookie);
                katana.UseOAuthBearerTokens(oAuthOptions);
                katana.UseTwitterAuthentication(twitterOptions);
            });

            owin.UseNancy();
        });
    }
}

public class Module : NancyModule
{
    public Module()
    {
        this.RequiresAuthentication();

        Get["/"] = _ => "Hello World!";
    }
}

public static class OwinExtensions
{
    public static AddMiddleware UseKatana(this AddMiddleware addMiddleware, Action<IAppBuilder> builderAction)
    {
        addMiddleware.Invoke(next =>
        {
            var appBuilder = new AppBuilder();

            appBuilder.Properties["builder.DefaultApp"] = next;
            appBuilder.Properties["host.AppName"] = "Whatever";

            builderAction.Invoke(appBuilder);

            return appBuilder.Build<AppFunc>();
        });

        return addMiddleware;
    }
}