homotopy hypothesis-theorem
delooping hypothesis-theorem
stabilization hypothesis-theorem
symmetric monoidal (∞,1)-category of spectra
A symmetric monoidal (weak) 2-category is a monoidal 2-category with a categorified version of a symmetry.
That is, it is a 2-category equipped with a tensor product 2-functor which satisfies all possible conditions for being commutative up to equivalence. In the language of k-tuply monoidal n-categories, a braided monoidal 2-category is a quadruply monoidal 2-category. As described there, this may be identified with a pointed 6-category with a single -morphism for . We can also say that it is a monoidal 2-category whose E1-algebra structure is refined to an E4-algebra structure.
symmetric monoidal 2-category, symmetric 3-group
Brian Day, Ross Street, Section 5 of: Monoidal Bicategories and Hopf Algebroids, Advances in Mathematics Volume 129, Issue 1, 15 July 1997, Pages 99-157 (doi:10.1006/aima.1997.1649)
Mike Shulman, Constructing symmetric monoidal bicategories (arXiv:1004.0993v1)
Last revised on July 21, 2021 at 16:33:58. See the history of this page for a list of all contributions to it.