A Freyd multicategory that has all tensor products and units, in a usual multicategorical sense that are preserved by , is equivalent to a Freyd category.
References
Sam Staton and Paul Blain Levy, Universal properties of impure programing languages. POPL ‘13: Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages, 2013, doi
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