It would be really useful if you could save a layer's symbology on AGOL or at least apply a layer file that you have created in ArcMap. Often I have a single dataset that contains multiple attributes, which I want to display differently. I realise I can copy the layer within a map and then symbolise it differently, but it would be really handy if I could save the symbology (and pop-ups and labels..?) as a layer file, so they could be easily applied to other maps. By saving as a layer file as opposed to creating a whole new dataset, it would help reduce file storage considerably.