Topos methods in the Foundations of Physics

This is a well written expository article summarising the topos approach to physics. In essence the claim is that general relativity and quantum mechanics live in different categories and that by building a new category for them both a unified theory should result. This is a commendable aim. I don’t do much in category theory but I am very well aware of the additional power and clarity that their use brings.

Fundamentally there seems to be no reason why this approach is different from the others, e.g. loop QG, string theory, NCG, or the spinor or causal set approaches. Demonstrating that such theories are the same would be a great deal of work, however.

The article gives a conceptual review of the topos approach focusing on Isham and Doring’s work. Plenty of references to follow up on!