[{"_id":1,"list_id":23,"name":"list01","cards":[{"id":3,"name":"card01","categories":[{id:10,category:"section01",tags:[{id:11,name:"tag01",is_selected:true}]},{id:10,category:"section02",tags:[{id:11,name:"tag01",is_selected:true}]}]}]},{"_id":2,"list_id":24,"name":"list01","cards":[{"id":3,"name":"card01","categories":[{id:10,category:"section01",tags:[{id:11,name:"tag01",is_selected:true}]}]}]}]

db.collection.update({"list_id":23,"cards.categories.category":"section01"},{$push:{"cards.$.categories.$[elem].tags":{name:"tag02",id:"123",is_selected:true}}},{arrayFilters:[{"elem.category":"section01"}],multi:true})