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Categorical aspects of the theory of modules over trusses are studied. Tensorproduct of modules over trusses is defined and its existence established. Inparticular, it is shown that bimodules over trusses form a monoidal category.Truss versions of the Eilenberg-Watts theorem and Morita equivalence areformulated. Projective and small-projective modules over trusses are definedand their properties studied.

On functors between categories of modules over trusses