Arity-reducibility conjecture for polyadic tensor categories with units

Let a polyadic ($n$-ary) tensor category be equipped with a unit object and unitors. Arity-reducibility conjecture. It should be arity-reducible to a binary category, with its $n$-ary product obtained by iterating a binary tensor product.

This is suggested by the corresponding reduction principle for $n$-ary groups, where the existence of units and neutral polyads permits reduction to binary groups. The source gives no evidence that the categorical claim has been proved or refuted.