A **Freyd multicategory** is to a multicategory as a Freyd category is to a monoidal category.

A **Freyd multicategory** consists of

- A multicategory $\mathcal{V}$ (usually cartesian)
- A premulticategory $\mathcal{C}$
- A functor $return : \mathcal{V}\to\mathcal{C}$ that is the identity on objects and preserves central morphisms.

A Freyd multicategory that has all tensor products and units, in a usual multicategorical sense that are preserved by $return$, is equivalent to a Freyd category.

- 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

Last revised on August 29, 2022 at 05:22:23. See the history of this page for a list of all contributions to it.