[{"teacher":"Ben","students":[{"name":"Liz","age":8,"pets":1},{"name":"Jon","age":9,"pets":3},{"name":"Eva","age":9,"pets":2}]}]

db.collection.aggregate([{"$match":{}},{"$project":{"_id":0,"teacher":1,"students":{"$filter":{input:"$students",cond:{"$eq":["$$this.age",9]}}}}},{"$unset":"students.age"}])