[{name:"a",type:"x",categories:[{type:"t1",name:"TestCategory1"}]},{name:"b",type:"y",categories:[{type:"t2",name:"TestCategory2"}]},{name:"c",type:"z",categories:[{type:"t3",name:"TestCategory3"}]}]

db.collection.find({"categories.name":{$in:["TestCategory1","TestCategory2"]}})