We discuss some ways in which topos theory (a branch of category theory) canbe applied to interpretative problems in quantum theory and quantum gravity. InSection 1, we introduce these problems. In Section 2, we introduce topostheory, especially the idea of a topos of presheaves. In Section 3, we discussseveral possible applications of topos theory to the problems in Section 1. InSection 4, we draw some conclusions.
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