Can Toby run on a mobile phone or a tablet?
Yes. Toby has an app for iPhone and iPad, and one for Android:
Sign in with your Toby account to browse your Spaces and collections, open the pages you saved, and search them. You can also save a link into a collection from your phone's share menu.
Saving your open tabs and sessions needs the full Toby: the Toby Chrome extension on a computer.