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Winui 3 Combobox in datagrid not displaying data

I am migrating a WPF app to WinUI3. Things went well until I needed to put a combo box in the datagrid. That MS had removed the datagrid from the standard tools was overcome with [Community Toolkit Controls](https://learn.microsoft.com/en-us/windows/communitytoolkit/controls/datagrid). 

I can make a column with a combobox, but I have not managed to link it correctly to the data I need to select from. Let's say that it is a page to display books with their primary genre in the combobox.

I use MVVM for connecting the view and data. Showing the main part of the data for the page works. However, the combobox for genres is empty.

The window:

    <Grid x:Name="RootGrid">
        <ctWUI3:DataGrid x:Name="tasksDataGrid"
                         AutoGenerateColumns="False" 
                         GridLinesVisibility="All"
                         CanUserSortColumns="True"
                         ScrollViewer.VerticalScrollBarVisibility="Auto"
                         AlternatingRowBackground="LightGray"
                         ItemsSource="{Binding Books}" 
                         Margin="10,0,5,0" 
                         RowDetailsVisibilityMode="VisibleWhenSelected">
            <ctWUI3:DataGrid.Columns>
                <ctWUI3:DataGridTextColumn Binding="{Binding Id}"
                            		Header="Name" 
									Width="150"
                            		IsReadOnly="False" />
                <ctWUI3:DataGridTextColumn Binding="{Binding Title}"
                            		Header="Name" 
									Width="150"
                            		IsReadOnly="False" />
                <ctWUI3:DataGridTextColumn Binding="{Binding Description}"
                            		Header="Description" 
									Width="150"
                            		IsReadOnly="False" />
                <ctWUI3:DataGridTextColumn Binding="{Binding PrimaryGenreId}"
                            		Header="Genre" 
									Width="150"
                            		IsReadOnly="False" />
                <ctWUI3:DataGridComboBoxColumn Binding="{Binding PrimaryGenreId}"
                                               Header="Genre" 
                                               ItemsSource="{Binding Genres, Mode=OneWay}"
                                               DisplayMemberPath="Name"
                                               Width="SizeToHeader" />
            </ctWUI3:DataGrid.Columns>
        </ctWUI3:DataGrid>
    </Grid>

The xaml.cs

    public sealed partial class MainWindow : Window
    {
        public MainWindow()
        {
            this.InitializeComponent();
            RootGrid.DataContext = new MainViewModel();
        }
    }

Then the MainViewModel.cs contains two private fields, a constructor of test data, and the public getter/setters for the fields.

    public ObservableCollection<Book> Books
    {
        get => _books;
        set { SetProperty(ref _books, value); }
    }

    public ObservableCollection<Genre> Genres
    {
        get => _genres;
        set { SetProperty(ref _genres, value); }
    }

How do I get the combobox to display the genre of the book for that row (using a GenreId field as the foreign key)?