* A monoid is the same as a category with a single object.
* A monoidal category is the same as a bi-category with a single object.
* A commutative monoid is the same as a bi-category with a single object and a single 1-morphism (This is essentially the Eckmann-Hilton argument).
* A braided monoidal category is the same as a tri-category with a single object and a single 1-morphism


and so on. This behavior of (multi)-degenerate n-categories is known as the [Periodic Table of n-categories](http://ncatlab.org/nlab/show/periodic+table).


Now it seems natural to ask: What about "degenerate $\infty$-categories$/(\infty,1)$-categories$/(\infty,n)$-categories"? A reasonable guess for example would be, that a $(\infty,2)$-category with a single object should give a [monoidal $(\infty,1)$-category](http://ncatlab.org/nlab/show/monoidal+(infinity,1)-category). This kind of question might already be answered somewhere in Jacob Lurie's papers, however, I have a hard time finding anything.


EDIT: To avoid confusion, with a bicategory I meant weak $2$-category, with a tricategory a weak $3$-category. I am mostly interested in the weak case, since the periodic table is less rich if we look at strict $n$-categories. When I talk about $(\infty,1)$-categories, I also mean in the weak sense. As a definition of a $(\infty,1)$-category take for example a simplicial set satisfying the inner horn filling condition.



The "$\infty$"-column in the periodic table of n-categories
The result that $E\_n$-monoidal $(\infty,m)$-categories are equivalent to pointed $(\infty,n+m)$-categories with a single object, 1-morphism, ..., and $n$-morphism (and the more general one that $E\_n$-algebras in an $E\_n$-monoidal $\infty$-category $\mathcal{V}$ are equivalent to pointed $(\infty,n)$-categories enriched in $\mathcal{V}$ with a single object, 1-morphism, etc.) can be found in section 6.3 of <http://arxiv.org/abs/1312.3178>.


