nLab
stabilization hypothesis

Contents

Idea

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

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

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

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)