  Tensor networks are generated by a set of small rank tensors and define
many-body quantum states in a succinct form. The corresponding map is not
one-to-one: different sets of tensors may generate the very same state. A
fundamental question in the study of tensor networks naturally arises: what is
then the relation between those sets? The answer to this question in one
dimensional setups has found several applications, like the characterization of
local and global symmetries, the classification of phases of matter and unitary
evolutions, or the determination of the fixed points of renormalization
procedures. Here we answer this question for projected entangled-pair states
(PEPS) in any dimension and lattice geometry, as long as the tensors generating
the states are normal, which constitute an important and generic class.
