db.myDb.aggregate(
{
    $group:{
        _id: {
            class_name : "$class",
            type_name : "$name"
        },
        items: {
            $addToSet : "$name"
        }
    }
},
{
    $group:{
        _id : "$_id.class_name",
        types : {
            $addToSet : {
                type : "$_id.type_name",
                items : "$items"
            }
        }
    }
})

{
    _id : "class A",
    types: [
        {
            type: "type 1",
            items: ["ObjectA1"]
        },
        {
            type: "type 2",
            items: ["ObjectA2_1", "ObjectA2_2"]
        }
    ]
},
{
    _id : "class B",
    types: [
        {
            type: "type 3",
            items: ["ObjectB3"]
        }
    ]
}