  Using the concept of variational tricomplex endowed with a presymplectic
structure, we formulate the general notion of symmetry. We show that each
generalized symmetry of a gauge system gives rise to a sequence of conservation
laws that are represented by on-shell closed forms of various degrees. This
extends the usual Noether's correspondence between global symmetries and
conservation laws to the case of lower-degree conservation laws and not
necessarily variational equations of motion. Finally, we equip the space of
conservation laws of a given degree with a Lie bracket and establish a
homomorphism of the resulting Lie algebra to the Lie algebra of global
symmetries.
