Mongodb 3.2 aggregation $lookup for nested document - mongodb

Question

I have two collections: memberships and categories.
In the categories I have stored array of objects called ageGroups.
memberships : [{
_id: ObjectId,
ageCategory: ObjectId,
ageGroup: ObjectId
}]
categories: {
_id: ObjectId,
ageGroups: [{
_id: ObjectId,
name: String
}, {
_id: ObjectId,
name: String
}, {
_id: ObjectId,
name: String
}]
}
There are ageCategory and ageGroup properties in memberships collection.
Now i need to aggregate these two and get result like this
[{
id: 'membership id here',
ageGroup: 'Age Group name here'
},{
id: '2 membership id here',
ageGroup: '2 membership age Group name here'
}]
So I tried
db.memberships.aggregate([
{
$lookup: {
from: 'categories', localField: 'ageCategory', foreignField: '_id', as: 'ageCategory'
}
},
{
$unwind: '$ageCategory'
},
{
$project: {
'group': {
$filter: {
input : '$ageCategory.ageGroups',
as : 'group',
cond : 'group._id' == '$_id'
}
}
}
},
{
$unwind: '$group'
},
{
$project: {
'group' : '$group.name'
}
}
]);
This query return empty result. As much as I understand, problem in filter condition
$filter: {
input : '$ageCategory.ageGroups',
as : 'group',
cond : 'group._id' == '$_id'
}
when I tried to set true in cond, it pushed new document to result, for each group, even if ageGroup not that, which is assigned to membership. Thanks for help!
UPD
I found solution,
{
$project: {
'group': {
$filter: {
input : '$ageCategory.ageGroups',
as : 'group',
cond : { $eq:['$$group._id', '$ageGroup']}
}
}
}
},
I have added double dollar sign with $eq operator and problem has been solved. Now I search better solution and I would like have a query which get similar result
{
"_id" : // member id,
"group" : "1-3 members"
}
{
"_id" : //member id,
"group" : "17-19 members"
}
without storing ageCategory in memberships table, only with ageGroup id.