[{"_id":"diamond","activities":[[{"term":"11","sport_name":"football"}]]},{"_id":"topaz","activities":[[{"term":"12","sport_name":"football"}],[{"term":"11","sport_name":"football"},{"term":"11","sport_name":"hand ball"}]]}]

db.collection.aggregate([{$project:{activities:{$arrayToObject:{$map:{input:"$activities",in:{k:{$arrayElemAt:["$$this.term",0]},v:"$$this"}}}}}}])