A way to save nested positions in an array MongoDB

Question

I have create the variable with value index position Card in database.

Problem is here with $set, can someone correct me query with use variable "position" please ???

And can We create query like this??

Because at this moment this query don't work. Can someone help me please?

EDIT

/* 1 */
{
    "_id" : ObjectId("59e0aa31daa273086bf100ae"),
    "name" : "2",
    "users" : [ 
        ObjectId("59cd114cea98d9326ca1c421")
    ],
    "lists" : [ 
        {
            "list" : "1",
            "cards" : [ 
                {
                    "name" : "dea"
                }
            ]
        }, 
        {
            "list" : "dea",
            "cards" : [ 
                {
                    "name" : "22222",
                    "Author" : [ 
                        "59df60fb6fad6224f4f9f22d", 
                        "59df60fb6fad6224f4f9f22d", 
                        "59df60fb6fad6224f4f9f22e"
                    ]
                }, 
                {
                    "name" : "fea"
                }
            ]
        }
    ],
    "__v" : 0
}

/* 2 */
{
    "_id" : ObjectId("59e35de8a8c83d1ab00dfcb9"),
    "name" : "2",
    "users" : [ 
        ObjectId("59cd114cea98d9326ca1c421")
    ],
    "lists" : [],
    "__v" : 0
}