[{name:"Enrico",age:32,items:[{type:"cat",color:"blue"},{type:"dog",color:"red"}]},{name:"Francesca",age:33,items:[{type:"foo",color:"bar"},{type:"hello",color:"world"}]},{name:"Mario",age:40,items:[{type:"cat",color:"green"},{type:"dog",color:"white"}]}]

db.collection.aggregate([{$set:{items:{$map:{input:"$items",in:{$mergeObjects:["$$this",{$cond:[{$eq:["$$this.type","cat"]},{color:"$name"},{}]}]}}}}}])