Issue: updating value inside the subdocument of a

Question

I am having some trouble trying to update some fields of a subdocument inside a subdocument in mongodb.

First of all, let's find exactly the document I need to update to see how the document structure looks like:

// query:
db.getCollection('collection').find({
    application: ObjectId("568b3a2feaa4171d03734776"),
    _id: ObjectId("568b3a2feaa4171d03734779"),
    status: 'sent',
    'mailingList.recipients.email': '[e-mail]' // an index
},
{
    'mailingList.$.recipients': true
});

// query result:
{
    "_id" : ObjectId("568b3a2feaa4171d03734779"),
    "mailingList" : [ 
        {
            "id" : 55,
            "recipients" : [ 
                {
                    "metadata" : {
                        "name" : "Example",
                        "surname" : "Example"
                    },
                    "email" : "[e-mail]",
                    "message" : {
                        "events" : []
                    }
                }
            ]
        }
    ]
}

What I would like to achieve is exactly being able to update any of the fields in the object inside recipients[]: let's say, for example, email. I've tried the following so far, using the $set operator:

db.getCollection('collection').update({
    application: ObjectId("568b3a2feaa4171d03734776"),
    _id: ObjectId("568b3a2feaa4171d03734779"),
    status: 'sent',
    'mailingList.recipients.email': '[e-mail]'
},
{
    $set: {
        'mailingList.$.recipients.email': '[e-mail]'
    }
});

but I get the following error:

cannot use the part (recipients of mailingList.1.recipients.email) to traverse the element ({recipients: [ { metadata: { name: "Example", surname: "Example" }, email: "[e-mail]", message: { events: [] } } ]})

What am I missing? I had already worked with embedded subdocuments before (not like this where there is a subdocument inside another subdocument) and using $set was enough to update any field inside a single subdocument, i.e:

$set: {
    'mailingList.$.email': '[e-mail]'
}