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.
An aspect of the proof of this for (n,1)-categories 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.
Section 5.1.2 of