Михаилушка

<DataGridComboBoxColumn x:Name="categoryComboBox" Header="Категории" ItemsSource="{Binding category}">
                                <DataGridComboBoxColumn.EditingElementStyle>
                                    <Style TargetType="{x:Type ComboBox}">
                                        <EventSetter Event="Loaded" Handler="CategoryComboBoxLoaded" />
                                    </Style>
                                </DataGridComboBoxColumn.EditingElementStyle>
                            </DataGridComboBoxColumn>

private void CategoryComboBoxLoaded(object sender, EventArgs e)
        {
            var categoryComboBox = sender as ComboBox;

            addDataAdapter = new MySqlDataAdapter
            {
                SelectCommand = new MySqlCommand()
                {
                    Connection = programQuery,
                    CommandText = "SELECT * FROM category"
                }
            };

            DataTable dtEmpName = addDataSet.Tables["category"];
            categoryComboBox.ItemsSource = ((IListSource)dtEmpName).GetList();
            categoryComboBox.SelectedValuePath = "id_category";
            categoryComboBox.DisplayMemberPath = "name_category";

            //var selectedItem = this.addDataGrid.CurrentItem;

            categoryComboBox.SelectedIndex = 0;

        }

<DataGridComboBoxColumn x:Name="testComboBox" ItemsSource="{Binding category}" Header="Категории" DisplayMemberPath="id_category" SelectedValuePath="name_category"/>

private void FilltestComboBox()
        {
            addDataAdapter = new MySqlDataAdapter
            {
                SelectCommand = new MySqlCommand()
                {
                    Connection = programQuery,
                    CommandText = "SELECT * FROM category"
                }
            };

            addDataAdapter.Fill(addDataSet, "category");
            DataTable dtEmpName = addDataSet.Tables["category"];
            testComboBox.ItemsSource = ((IListSource)dtEmpName).GetList();
            testComboBox.SelectedValuePath = "id_category";
            testComboBox.DisplayMemberPath = "name_category";

        }