Stabilization hypothesis

In mathematics, specifically in category theory and algebraic topology, the Baez–Dolan stabilization hypothesis, proposed in {{harv|Baez|Dolan|1995}}, states that suspension of a weak n-category has no more essential effect after n + 2 times.{{cite arXiv|last=Lurie|first=Jacob|date=2009-10-30|title=Derived Algebraic Geometry VI: E_k Algebras|eprint=0911.0018|language=en|at=Example 1.2.3|class=math.AT}} Precisely, it states that the suspension functor $\backslash mathsf\{nCat\}\_k\; \backslash to\; \backslash mathsf\{nCat\}\_\{k+1\}$ is an equivalence for $k\; \backslash ge\; n\; +\; 2$.{{harvnb|Baez|Dolan|1995|loc=§ 5}}