Stabilization hypothesis

In mathematics, specifically in category theory and algebraic topology, the Baez–Dolan stabilization hypothesis, proposed in (Baez & Dolan 1995), states that suspension of a weak n-category has no more essential effect after n + 2 times.[1] Precisely, it states that the suspension functor n C a t k → n C a t k + 1 {\displaystyle {\mathsf {nCat}}_{k}\to {\mathsf {nCat}}_{k+1}} is an equivalence for k ≥ n + 2 {\displaystyle k\geq n+2} .[2]

References

  1. ^ Lurie, Jacob (2009-10-30). "Derived Algebraic Geometry VI: E_k Algebras". Example 1.2.3. arXiv:0911.0018 [math.AT].
  2. ^ Baez & Dolan 1995, § 5

Sources

  • Baez, John C.; Dolan, James (1995), "Higher-dimensional algebra and topological quantum field theory", Journal of Mathematical Physics, 36 (11): 6073–6105, arXiv:q-alg/9503002, Bibcode:1995JMP....36.6073B, doi:10.1063/1.531236, MR 1355899, S2CID 14908618
  • https://ncatlab.org/nlab/show/stabilization+hypothesis


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