How to collate teams by a property of the leader, in MongoDB - mongodb

Question

I have a database with some users, who belong to teams. Each team has a leader. Each user has a subject.
I want to collate teams by the leader's subject.
My data looks like this:
db={
"teams": [
{
_id: "t1",
members: [
{
"_id": "u1",
"leader": true
},
{
"_id": "u2"
},
{
"_id": "u3"
}
],
},
{
_id: "t2",
members: [
{
"_id": "u2",
"leader": true
},
{
"_id": "u4"
}
],
},
{
_id: "t3",
members: [
{
"_id": "u1",
"leader": true
},
{
"_id": "u4"
}
],
},
{
_id: "t4",
members: [
{
"_id": "u2",
"leader": true
}
],
},
],
"users": [
{
"_id": "u1",
"subject": "history"
},
{
"_id": "u2",
"subject": "maths"
},
{
"_id": "u3",
"subject": "geography"
},
{
"_id": "u4",
"subject": "french"
}
]
}
The result I want is:
{
"history": ["t1", "t3"],
"maths": ["t2", "t4"]
}
I have an aggregation that gets me the _id of every leader, and from there I can get the result I want in stages, by first finding the subject of every leader, then going back through the projects and assigning a subject to each project based on the identify of the leader. It works but it is inelegant and I think it will be slow. It seems to me there should be some better way to do this, maybe something like a join?
Is there a nifty way to get the result I want from a single MongoDB operation?
Here is a Mongo Playground with my data:
https://mongoplayground.net/p/SIJv9-hVNzJ
Many thanks for any help.
Edit: my test data are confusing because '_id' is used in both collections, making it hard to unpack the answer. Here is an updated Mongo Playground that uses different key names for each collection and helped me to understand the perfect answer.

Answer 1

Yes, you should join your collections on users._id with a $lookup, and then transform value to key with $arrayToObject (introduced in Mongodb 3.4.4)
Here is a possible way to do this :
db.teams.aggregate([
{
"$unwind": "$members"
},
{
"$match": {
"members.leader": true
}
},
{
"$lookup": {
"from": "users",
"localField": "members._id",
"foreignField": "_id",
"as": "users"
}
},
{
"$unwind": "$users"
},
{
"$group": {
"_id": "$users.subject",
"team": {
"$push": "$_id"
}
}
},
{
"$replaceRoot": {
"newRoot": {
"$arrayToObject": [
[
{
k: "$_id",
v: "$team"
}
]
]
}
}
}
])
try it online: mongoplayground.net/p/TuEpMzHkI-0