  Derived brackets as introduced and studied by Kosmann-Schwarzbach and Voronov
are a powerful tool for describing and understanding infinitesimal symmetry
actions relevant in physics. Roytenberg and Weinstein showed that this
continues to hold for the categorified symmetries arising in Hitchin's
generalized geometry. After reviewing some well-established examples, we prove
that derived brackets also underlie the symmetries of Double Field Theory and
heterotic Double Field Theory. This leads to a common framework for large
classes of symmetries, which suggests that derived bracket constructions can
function as a guiding principle in the description of infinitesimal actions of
symmetries in physics. As a new result, we present sufficient conditions on a
bracket to give rise to a Lie 2-algebra of symmetries via antisymmetrized
derived brackets.
