Observations
from flux compactifications of closed string theory suggest that a
theory of gravity at quantum scales may be not only noncommutative but
also nonassociative. Having an abstract understanding of geometry is one
approach to help us to describe a noncommutative and nonassociative
theory of gravity. In work together with Alexander Schenkel and Richard
J. Szabo we have appealed to the tools of category theory to better
understand the mathematical structures underlying noncommutative and
nonassociative deformations of spacetime geometry.
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