Finitely presented promonoidal structures on an additive category extend uniquely to right exact monoidal structures on the associated Freyd category, equivalently on finitely presented functors.
Tensor structure for Nori motives
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abstract
We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative construction for the tensor product on Nori motives.
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Tensor products of finitely presented functors
Finitely presented promonoidal structures on an additive category extend uniquely to right exact monoidal structures on the associated Freyd category, equivalently on finitely presented functors.