  The gauge theories underlying gauged supergravity and exceptional field
theory are based on tensor hierarchies: generalizations of Yang-Mills theory
utilizing algebraic structures that generalize Lie algebras and, as a
consequence, require higher-form gauge fields. Recently, we proposed that the
algebraic structure allowing for consistent tensor hierarchies is axiomatized
by `infinity-enhanced Leibniz algebras' defined on graded vector spaces
generalizing Leibniz algebras. It was subsequently shown that, upon appending
additional vector spaces, this structure can be reinterpreted as a differential
graded Lie algebra. We use this observation to streamline the construction of
general tensor hierarchies, and we formulate dynamics in terms of a hierarchy
of first-order duality relations, including scalar fields with a potential.
