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.
A constructive approach to Freyd categories
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abstract
In this paper we give an algorithmic description of Freyd categories that subsumes and enhances the usual approach to finitely presented modules in computer algebra. The upshot is a constructive approach to finitely presented functors that only relies on a few basic algorithms.
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2019 1verdicts
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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.