Some Possible Roles for Topos Theory in Quantum Theory and Quantum Gravity

We discuss some ways in which topos theory (a branch of category theory) can be applied to interpretative problems in quantum theory and quantum gravity. In Section 1, we introduce these problems. In Section 2, we introduce topos theory, especially the idea of a topos of presheaves. In Section 3, we discuss several possible applications of topos theory to the problems in Section 1. In Section 4, we draw some conclusions. Submitted to Foundations of Physics for an issue in honour of Marisa Dalla Chiara. Based on a lecture given by CJI at the conference Towards a New Understanding of Space, Time and Matter , University of British Columbia, Canada (1999). email: [email protected] email: [email protected]