How to use $elemMatch on aggregate's projection?

For some reason $elemMatch doesn't work in aggregations. You need to use the new $filter operator in Mongo 3.2. See https://docs.mongodb.org/manual/reference/operator/aggregation/filter/

Actually, the simplest solution is to just $unwind your array, then $match the appropriate documents. You can wind-up the appropriate documents again using $group and $push.

The answer to this question maybe help.

db.collection_name.aggregate({
    "$match": {
        "complist": {
            "$elemMatch": {
                "a": "a"
            }
        }
    }
});