It is overall better for the health of any field to welcome outsiders with new ideas. You seem quite skeptical of the role of sheaves in consensus and security, as I would expect any scientist to be. However in general for that sort of criticism to be accurate you need deep knowledge in both areas. You haven’t given me the impression that you actually understand sheaves or categories at a deep level (not saying that you don’t, just that our interaction hasn’t signaled that) and are instead essentially insisting that “the old ways are best” and that since I do not practice them I have nothing to contribute. Welcoming outsiders is how you get the largest volume of new ideas, and if you refuse contribution from outsiders you stunt your own field.
Sheaves already behave something like consensus mechanisms. Does this manifold permit a spin structure? Let’s ask the small open sets. How many holes does this variety have? Let’s check the sheaf cohomology. What dimension is the ground space of this quantum system? Well, we can count the number of solutions to a differential equation living in some sheaf… These are how we go from local to global information. If that doesn’t scream consensus at you, I cannot help you.
