Running ASP.NET Core within IIS

AspNetCoreOwinMiddleware.cs

public class AspNetCoreOwinMiddleware<TAspNetCoreStartup> : OwinMiddleware, IServer
    where TAspNetCoreStartup : class
{
    private readonly IWebHost _webHost;
    private Func<IOwinContext, Task> _appFunc;

    IFeatureCollection IServer.Features { get; } = new FeatureCollection();

    public AspNetCoreOwinMiddleware(OwinMiddleware next, IAppBuilder app)
        : base(next)
    {
        var appProperties = new AppProperties(app.Properties);
        if (appProperties.OnAppDisposing != default(CancellationToken))
            appProperties.OnAppDisposing.Register(Dispose);

        _webHost = new WebHostBuilder()
            .ConfigureServices(s => s.AddSingleton<IServer>(this))
            .UseStartup<TAspNetCoreStartup>()
            .Build();

        _webHost.Start();
    }

    void IServer.Start<TContext>(IHttpApplication<TContext> application)
    {
        _appFunc = async owinContext =>
        {
            var features = new FeatureCollection(new OwinFeatureCollection(owinContext.Environment));

            var context = application.CreateContext(features);
            try
            {
                await application.ProcessRequestAsync(context);
                application.DisposeContext(context, null);
            }
            catch (Exception ex)
            {
                application.DisposeContext(context, ex);
                throw;
            }
        };
    }

    public override Task Invoke(IOwinContext context)
    {
        if (_appFunc == null)
            throw new InvalidOperationException("ASP.NET Core Web Host not started.");

        return _appFunc(context);
    }

    public void Dispose()
    {
        _webHost.Dispose();
    }
}

AspNetCoreStartup.cs

public class AspNetCoreStartup
{
    public void ConfigureServices(IServiceCollection services)
    {
        services.AddMvc();
    }

    public void Configure(IApplicationBuilder app)
    {
        app.UseMvc();
    }
}

OwinStartup.cs

[assembly: OwinStartup(typeof(OwinStartup))]

public class OwinStartup
{
    public void Configuration(IAppBuilder app)
    {
        // Paths in ASP.NET Core will not start with /api but with /
        app.Map("/api", subApp => subApp.Use<AspNetCoreOwinMiddleware<AspNetCoreStartup>>(app));
    }
}