  Topological T-duality correspondences are higher categorical objects that can
be classified by a strict Lie 2-group. In this article we compute the
categorical automorphism group of this 2-group; hence, the higher-categorical
symmetries of topological T-duality. We prove that the categorical automorphism
group is a non-central categorical extension of the integral split
pseudo-orthogonal group. We show that it splits over several subgroups, and
that its k-invariant is 2-torsion.
