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{\bf L\'aszl\'o Lov\'asz and Alexander Schrijver}
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{\bf Semidefinite Functions on Categories}
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Freedman, Lov\'asz and Schrijver characterized graph parameters that
can be represented as the (weighted) number of homomorphisms into a
fixed graph. Several extensions of this result have been proved. We
use the framework of categories to prove a general theorem of this
kind. Similarly as previous resuts, the characterization uses certain
infinite matrices, called {\it connection matrices}, which are
required to be positive semidefinite.

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