ScalingStacks

Example 15.5. By [25], the Joyal model category of simplicial sets is a model category of $(\infty,1)$-categories. More generally, all of the following model categories are model categories of $(\infty,1)$-categories:

1. (a)

   the Joyal model category of quasicategories $\mathrm{QCat}$ [15, 24, 28],

2. (b)

   the Rezk model category of complete Segal spaces $\CSS$ [33],

3. (c)

   the Bergner model category of simplicial categories [18, 11],

4. (d)

   the Tamsamani–Hirschowitz–Simpson–Pellissier model categories of Segal Categories [19, 22, 32, 10, 37, 12],

5. (e)

   the Barwick–Kan model category of relative categories [6].