I seem to recall that these papers were not particularly mathematically sophisticated, but one element stood out: whereas a classical principle bundle looks the same at every point, the deformation parameter in a quantum bundle may easily vary from point to point. Even in those days, people thought a lot about relating deformation parameters to $\hbar$. This was all just a mathematical curiosity, until it became clear that some tough (and extremely interesting) algebraic geometry, and other mathematics, lay at the bottom of it. (Of course, all roads led to category theory in the end).
Algebraic geometers love spaces with extra structure which varies from point to point. They talk about spectra (usually of rings) and we need not be afraid of these gadgets because they are naturally specified by a functor from a suitable category of algebras into a category of spaces. And it turns out that this functor is best understood from the point of view of a special topos, because the weird topologies that algebraic geometers like to use are neatly encoded by axioms of Grothendieck. (In fact, this is where the idea of a topos comes from in the first place).
At the time, I believe it was Zamolodchikov who advised me to ditch lattice gauge theory (which I was supposed to be doing) for something more interesting. In the end, I did give up the lattice gauge theory, but I can't say it was because I listened to anybody's advice. (And as it turns out, lattice gauge theory has actually done rather well over the last decade).