nLab
stabilization hypothesis

Idea

The Baez-Dolan stabilization hypothesis states that for all $k=n+2$ a k-tuply monoidal n-category is “maximally monoidal”. In other words, for $k\ge n+2$, a $k$-tuply monoidal $n$-category is the same thing as an $(n+2)$-tuply monoidal $n$-category. More precisely, the natural inclusion $k\mathrm{Mon}n\mathrm{Cat}\hookrightarrow (n+2)\mathrm{Mon}n\mathrm{Cat}$ is an equivalence of higher categories.

Proof for $(n\mathrm{,1})$-categories

For the case of monoideal (n,1)-categories a proof of the stabilization hypothesis appears in

• Jacob Lurie, $𝔼[k]$-Algebras (stabilization hypothesis)