Higher category theory
higher category theory
Extra properties and structure
The (large) -category is the collection of all (small) (∞,n)-categories:
There are various presentations for this. For general see for instance this section at Theta-space. For low see the discussion at (∞,1)Cat and (∞,2)Cat?.
Often it is useful to consider just the maximal (∞,1)-category inside . This is what is presented by various model category structures on models for -categories.
The discussion in (BarwickSchommer-Pries) shows that essentially all proposed models for are in fact equivalent.
The automorphism ∞-group of is equivalent to .
This is due to (BarwickSchommer-Pries).