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Freedman, Lovasz and Schrijver characterized graph parameters that can be rep- resented 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 characteri- zation uses certain infinite matrices, called connection matrices, which are required to be positive semidefinite.

Semidefinite Functions on Categories