db={"stores":[{name:"store1",category:"category1"},{name:"store2",category:"category2"}],"products":[{store_name:"store1",name:"product1"},{store_name:"store2",name:"product2"}]}

db.products.aggregate([{"$lookup":{"from":"stores","localField":"store_name","foreignField":"name","as":"store"}},{"$set":{"store":{"$first":"$store"}}},{"$match":{"store.category":{"$ne":"category1"}}}])