Model categories and their localizations

By Philip S. Hirschhorn. 2003

1,731 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/575e7811adedd86028bf3cf7f94136ff7af590ee

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In Mathematical Physics

Citations in the corpus

Parametrized homotopy theory (2004, background): “The standard definition of cylinder objects in [73, 75, 139] requires i to be a cofibration.”
Manifold-theoretic compactifications of configuration spaces (2003, background): “X ← −−− − Y − −−− → Z, where the vertical maps are equivalences and at least one map on each of the horizontal levels is a cofibration, then the induced map of pushouts is an equivalence (see Theorem 13.5.4 in [ 13 ]).”
A Survey of (∞, 1)-Categories (2010, background): “We refer the reader to [13], [15], [17], or the original [25] for these axioms.”
Pro-categories in homotopy theory (2015, methodology): “2 Note that our definition of a model category is weaker than the one given in [Hi03], because we do not require the factorizations to be functorial.”
HZ -algebra spectra are differential graded algebras (2002, background): “See [Hov01, Section 2] for a brief summary of Bousfield localization; the definitive reference is [ Hir00 ].”
Strict Model Structures for Pro-categories (2001, background): “The original reference is [25], but we follow the notation and terminology of [14] as closely as possible.”
An Atiyah-Hirzebruch spectral sequence for KR-theory (2003, background): “[H]), we are localizing TopG at the set of maps {A → ∗|A ∈ A} and PA is the localization functor.”
Props in model categories and homotopy invariance of structures (2008, methodology): “We refer to the books [22, 24] for more details on the recollections of §§2.”
Derived smooth manifolds (2008, background): “[11] for an introduction to this subject), then the full subcategory of cofibrant-fibrant objects is a simplicial category in which all mapping spaces are fibrant.”
A cartesian presentation of weak n–categories (2009, methodology): “We refer to Hirschhorn [9] for background on homotopy colimits.”
Moduli of objects in dg-categories (2005, background): “he next section for the deﬁnition of the D−-stack MT and for the proof of its geometricity. The ﬁrst paragraph on model categories seem to be of a folklore knowledge and is essentially extracted from [Hi]. In the second paragraph we review some terminology and results concerning dg-categories. Most ”