  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.
