# Contents

## 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 $k \geq n + 2$, a $k$-tuply monoidal $n$-category is the same thing as an $(n+2)$-tuply monoidal $n$-category. More precisely, the natural inclusion $k Mon n Cat \hookrightarrow (n+2) Mon n Cat$ is an equivalence of higher categories.

## Proof for $(n,1)$-categories

An aspect of the proof of this for (n,1)-categories was demonstrated in

• Carlos Simpson, On the Breen-Baez-Dolan stabilization hypothesis for Tamsamani’s weak $n$-categories (arXiv:math/9810058)

in terms of Tamsamani n-categories?.

A proof of the full statement in terms of quasi-categories is sketched in section 43.5 of

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.

## References

Section 5.1.2 of

Revised on February 10, 2012 00:04:05 by Urs Schreiber (89.204.130.229)