Category Theory and Lightweight Ontology: Many Worlds, or Many Structures?

The ontological commitment of the many-worlds interpretation of quantum mechanics looks fairly heavy, and it is highly challenging how to make sense of the ontology of many worlds. Although some physicists and philosophers take the existence of many worlds at face value, there seems to be an ontologically less demanding way to circumvent the ontological heaviness of the many-worlds interpretation. And this is where the idea of structure comes into the play. The major tenet of this work is that structure paves the way for "ontology-lite", both in mathematical and physical contexts, and that this structure cannot be set-theoretical. I will argue for these ideas by interweaving philosophy of mathematics, such as Parsons' structuralist conception of mathematical entities, with philosophy of physics, such as structural realism, on the basis of category theory, which philosophers, apart from some recent exceptions, have not yet paid due attention to.