  We introduce quantum homomorphisms between quantum hypergraphs through the
existence of perfect strategies for quantum non-local games, canonically
associated with the quantum hypergraphs. We show that the relation of
homomorphism of a given type satisfies natural analogues of the properties of a
pre-order. We show that quantum hypergraph homomorphisms of local type are
closely related, and in some cases identical, to the TRO equivalence of finite
dimensionally acting operator spaces, canonically associated with the
hypergraphs.
