The Baez-Dolan stabilization hypothesis states that for all a k-tuply monoidal n-category is “maximally monoidal”. In other words, for , a -tuply monoidal -category is the same thing as an -tuply monoidal -category. More precisely, the natural inclusion is an equivalence of higher categories.
More generally, we can state a version for (n,k)-categories?: an -tuply monoidal -category is maximally monoidal.
An aspect of the proof of this when (i.e. that -tuply monoidal -categories are maximally monoidal) was demonstrated in
in terms of Tamsamani n-categories?.
Probably the first full proof in print is given in
where it appears in example 1.2.3 as a direct consequence of a more general statement, corollary 1.1.10.
A proof of the general form for arbitrary , using iterated -categorical enrichment to define -categories, is in
Section 5.1.2 of