n-stacks as a category of fibrant objects

Ezra Getzler – 8 August 2012

Let V be a category with finite limits, provided with a subcategory C (of covers) such that if gf is a cover and f is a cover, then g is a cover. Given a natural number n, we define a category of simplicial objects in V, called n-stacks, and prove that they form a category of fibrant objects. We then discuss the Dwyer-Kan simplicial localization of the category of n-stacks with respect to weak equivalences.