The renormalisation group allows you to consider what happens to a model when considered on different spatial scales. It is not a group, reflecting the fact that you can always move to a larger spatial scale, but recovering the smaller spatial scales may not be well-defined.
In category theory, localisation is a way to add inverse morphisms into a category, constraining some of its morphisms to be isomorphisms.
I was wondering what happens if you try to localise a renormalisation group?
Is this possible? Do you recover an actual group - and if so, how much information does it retain from the original renormalisation group?