A model category structure on the category of simplicial categories

By Julia E. Bergner. 2004

281 citations recorded by the source corpus.

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 of categories.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7405e3df870f8eba640f368e9d55b85e0ad8c53c

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On the algebraic K‐theory of higher categories (2012, background): “(1) One may form the hammock localization L(C,wC) [21]; then a relative nerve can be constructed as the simplicial nerve of the natural functor C R(L(C,wC)), where R denotes any fibrant replacement for the Bergner model structure [8].”
∞-Categories for the Working Mathematician (2018, background): “11 are the generating cofibrations in the Bergner model structure on simplicial categories [4].”
Dendroidal sets and simplicial operads (2011, background): “J. Bergner, ‘A model category structure on the category of simplicial categories’, Trans.”
The 2-category theory of quasi-categories (2013, unknown): “id[1] · ⎞ ⎟⎟⎠ Applying k, the 2-simplex k(f · σ0, σ1) of A witnesses the fact that k(f, id[1]) is a composite of k(f, σ0) and k((f · δ1) · σ0, id[1]).”
A universal characterization of higher algebraic K-theory (2010, methodology): “Here the model structure on the top is Bergner–Dwyer–Kan’s model structure on simplicial categories [7] and the model structure on the bottom is Joyal’s model structure on simplicial sets.”
Dwyer–Kan homotopy theory of enriched categories (2012, background): “6], for example, Bergner [4] for V the category of simplicial sets, Tabuada [28, 29] for V the categories of chain complexes over a commutative ring and symmetric spectra with the stable model structure [13], and Amrani [1] for V = Top the category of weakly Hausdorff compactly generated topological”
Higher Topos Theory (2006, methodology): “There exists a model structure on the category Cat∆ of (small) simplicial categories, which was constructed by Bergner ([7]).”
Categorical Homotopy Theory (2014, background): “There is a model structure on the category sSet-Cat of simplicially enriched categories and simplicially enriched functors due to Julia Bergner [Ber07].”
Rigidification of quasi-categories (2009, methodology): “In view of the generating cofibrations for sCat (see [3]), it is easy to show that U takes monomorphisms to cofibrations.”
Homotopy Theory of Higher Categories: THE MODEL STRUCTURE (2010, methodology): “the model category structure for simplicial categories ([87], now [88]), pointed out by Toen and subsequently fixed for simplicial categories by Bergner [33].”