(infinity, n)-Cat as a closed model category
I introduce two closed model categories of (∞, n)-precategories in which the fibrant objects are precisely the (∞, n)-categories. The first of these is generalized from Rezk's theory of complete Segal spaces. The latter is a slight variation of the Hirschowitz-Simpson theory of Segal n-categories. These closed model categories are expected to be Quillen equivalent, and the latter is Quillen equivalent to the Hirschowitz-Simpson closed model category of Segal n-precategories. I define closed model categories of symmetric monoidal (∞, n)-categories and (∞, n)-stacks relative to any of these closed model categories. I use heavily the previously undeveloped technique of enriched Bousfield localizations to construct these model categories. ^
Barwick, Clark, "(infinity, n)-Cat as a closed model category" (2005). Dissertations available from ProQuest. AAI3165639.