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A model category structure on the category of simplicial categories
In this paper we put a cofibrantly generated model category struc- ture on the category of small simplicial categories. The weak equivalences are a simplicial analogue of the notion of equivalence ofExpand
THREE MODELS FOR THE HOMOTOPY THEORY OF HOMOTOPY THEORIES
Abstract Given any model category, or more generally any category with weak equivalences, its simplicial localization is a simplicial category which can rightfully be called the “homotopy theory” ofExpand
A Survey of (∞, 1)-Categories
In this paper we give a summary of the comparisons between different definitions of so-called (∞, 1)-categories, which are considered to be models for ∞-categories whose n-morphisms are allExpand
Rigidification of algebras over multi-sorted theories
We define the notion of a multi-sorted algebraic theory, which is a generalization of an algebraic theory in which the objects are of different "sorts." We prove a rigidification result forExpand
Complete Segal spaces arising from simplicial categories
In this paper, we compare several functors which take simplicial categories or model categories to complete Segal spaces, which are particularly nice simplicial spaces which, like simplicialExpand
Homotopy limits of model categories and more general homotopy theories
Generalizing a deflnition of homotopy flber products of model cat- egories, we give a deflnition of the homotopy limit of a diagram of left Quillen functors between model categories. As has beenExpand
Simplicial monoids and Segal categories
Much research has been done on structures equivalent to topological or simplicial groups. In this paper, we consider instead simplicial monoids. In particular, we show that the usual model categoryExpand
The edgewise subdivision criterion for 2-Segal objects
We show that the edgewise subdivision of a $2$-Segal object is always a Segal object, and furthermore that this property characterizes $2$-Segal objects.
A CHARACTERIZATION OF FIBRANT SEGAL CATEGORIES
In this note we prove that Reedy fibrant Segal categories are fi- brant objects in the model category structure SeCatc. Combining this result with a previous one, we thus have that the fibrantExpand
Models for $(\infty, n)$-categories and the cobordism hypothesis
In this paper we introduce the models for $(\infty, n)$-categories which have been developed to date, as well as the comparisons between them that are known and conjectured. We review the role ofExpand
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