Model categories and their localizations

  title={Model categories and their localizations},
  author={Philip S. Hirschhorn},
Localization of model category structures: Summary of part 1 Local spaces and localization The localization model category for spaces Localization of model categories Existence of left Bousfield localizations Existence of right Bousfield localizations Fiberwise localization Homotopy theory in model categories: Summary of part 2 Model categories Fibrant and cofibrant approximations Simplicial model categories Ordinals, cardinals, and transfinite composition Cofibrantly generated model categories… Expand
Calculus of functors and model categories
The category of small covariant functors from simplicial sets to simplicial sets supports the projective model structure [5]. In this paper we construct various localizations of the projective modelExpand
On equivariant homotopy theory for model categories
We introduce and compare two approaches to equivariant homotopy theory in a topological or ordinary Quillen model category. For the topological model category of spaces, we generalize Piacenza'sExpand
Simplicial model category structures on the category of chain functors
The model structure on the category of chain functors Ch, developed in [4], has the main features of a simplicial model category structure, taking into account the lack of arbitrary (co-)limits inExpand
Homotopy Limit Functors on Model Categories and Homotopical Categories
Model categories: An overview Model categories and their homotopy categories Quillen functors Homotopical cocompleteness and completeness of model categories Homotopical categories: Summary of partExpand
Maps and localizations in the category of Segal spaces
The category of Segal spaces was proposed by Charles Rezk in 2000 as a suitable candidate for a model category for homotopy theories. We show that Quillen functors induce morphisms in this categoryExpand
A characterization of simplicial localization functors and a discussion of DK equivalences
Abstract In a previous paper, we lifted Charles Rezk’s complete Segal model structure on the category of simplicial spaces to a Quillen equivalent one on the category of “relative categories”. Here,Expand
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
Covariant Model Structures and Simplicial Localization
In this paper we prove that for any simplicial set $B$, there is a Quillen equivalence between the covariant model structure on $\mathbf{S}/B$ and a certain localization of the projective modelExpand
Simplicial model structures on pro-categories
We describe a method for constructing simplicial model structures on ind- and pro-categories. Our method is particularly useful for constructing "profinite" analogues of known model categories. OurExpand
Calculus of functors and model categories, II
The category of small covariant functors from simplicial sets to simplicial sets supports the projective model structure [B. Chorny, W.G. Dwyer, Homotopy theory of small diagrams over largeExpand


Acyclic Models and Triples
We shall prove two theorems on the “triple” cohomology of algebras [1] using a method of acyclic models suggested by H. Appelgate. Specifically, we show that the triple cohomology coincides withExpand
Locally presentable and accessible categories, London Math
  • Soc. Lecture Note Series, vol. 189, Cambridge University Press, Cambridge,
  • 1994
Rosicky, Locally presentable and accessible categories
  • London Math. Soc. Lecture Note Series,
  • 1994
Idempotent functors in homotopy theory, Manifolds—Tokyo 1973 (Proc
  • Internat. Conf., Tokyo, 1973), Univ. Tokyo Press, Tokyo,
  • 1975
Idempotent functors in homotopy theory, Manifolds—Tokyo
  • (Proc. Intern a l Conf.,
  • 1973
Dugundji, Categorical homotopy and fibrations
  • Trans. Amer. Math. Soc
  • 1969
Acyclic models and triples, Proceedings of the Conference on Categorical Algebra, La Jolla, 1965 (S
  • Eilenberg, D. K. Harrison, S. MacLane, and H. Röhrl, eds.), Springer-Verlag,
  • 1966