Is there any software that lets one explore group theory, ring theory, and category theory visually and theoretically that is tailored for education purposes? I'm not talking about using software like maple or mathematica but something more specific for learning and retention of ideas.
Something sorta like geogebra but for algebra. Something that lets one take some group(either built in or user-defined) and mess around with it to see what we learn at work. It should be highly visual and do all the heavy lifting.