Replacing model categories with simplicial ones

By Daniel Dugger. 2001

129 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7fbde8692be4c1006ab213040637171bc4780eac

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Universal Homotopy Theories (2000, methodology): “cofibration, fibration) precisely when D2 → D1 is a weak equivalence (resp.”
Morita theory in abelian, derived and stable model categories (2003, unknown): “egory; that construction does however not yield symmetric spectra, and there is no good composition pairing. The condition of being a simplicial model category can be removed by appealing to [RSS] or [Dug] where suitable model categories are replaced by Quillen equivalent simplicial model categories”
Higher quasi-categories vs higher Rezk spaces (2012, background): “2 of [20]) that (F,G) is a Quillen pair.”
Stable model categories are categories of modules (2003, background): “In [11], Dugger obtains the same conclusion under somewhat different hypotheses.”
Categorical Homotopy Theory (2014, background): “For example, one theorem says that any left proper, combinatorial model category is Quillen equivalent to a simplicial model category [Dug01].”
HZ -algebra spectra are differential graded algebras (2002, methodology): “prolongation preserves fibrations and weak equivalences between fibrant objects because they are levelwise fibrations and levelwise weak equivalences [ Du01a , A.3].”
On Voevodsky's algebraic K-theory spectrum BGL (2007, background): “In the stable homotopy category, which is additive, one may take the difference of f and g, and thus describe colimi≥0 D (i) via the distinguished triangle”
Uniqueness of the multiplicative cyclotomic trace (2011, background): “To see this, recall that the combinatorial model category C is Quillen equivalent to a simplicial model category C [10].”
Combinatorial Model Categories Have Presentations (2000, methodology): “(ii) Sufficiently large filtered colimits of weak equivalences are again weak equivalences: if λ is a sufficiently large regular cardinal,I is a λ-filtered indexing category, and if D1, D2: I → C are diagrams with a natural weak equivalence D1 → D2, then colim D1 → colim D2 is also a weak equivale”