## On (enriched) left Bousfield localizations of model categories (2007)

Citations: | 7 - 3 self |

### BibTeX

@MISC{Barwick07on(enriched),

author = {Clark Barwick},

title = {On (enriched) left Bousfield localizations of model categories},

year = {2007}

}

### OpenURL

### Abstract

by

### Citations

202 | Model Categories - Hovey - 1999 |

179 | Model categories and their localizations - Hirschhorn - 2003 |

64 | Accessible categories: the foundations of categorical model theory, volume 104 of Contemporary Mathematics - Makkai, Paré - 1989 |

60 |
Sheafifiable homotopy model categories
- Beke
(Show Context)
Citation Context ... a given small set of (trivial) cofibrations with cofibrant domain. This leads to the notion of tractable model categories. Most of the results have satisfactory proofs in print; the first section of =-=[3]-=- in particular is a very nice reference. (1) 1.1. — Suppose here X a universe. Notation 1.2. — Suppose C a model X-category. (1.2.1) Write wC (respectively, cof C, fibC) for the lluf subcategories com... |

51 |
D.M.: Calculating simplicial localizations
- Dwyer, Kan
- 1980
(Show Context)
Citation Context ... L H M whose objects are exactly those of M, with Mor L H M(X, Y ) = colimn ν•(w Mor n M(X, Y )) for any objects X and Y . The standard references on the hammock localization are the triple of papers =-=[6]-=-, [7], and [8] of W. G. Dwyer and D. Kan. A more modern treatment can be found in [9].� �� � � �� � � � � � 14 CLARK BARWICK Scholium 2.3 (Dwyer–Kan). — Suppose Q : M �Mc a cofibrant replacement func... |

50 | Combinatorial model categories have presentations - Dugger |

33 |
Homotopy limit functors on model categories and homotopical categories, volume 113
- Dwyer, Hirschhorn, et al.
- 2004
(Show Context)
Citation Context ...n M(X, Y )) for any objects X and Y . The standard references on the hammock localization are the triple of papers [6], [7], and [8] of W. G. Dwyer and D. Kan. A more modern treatment can be found in =-=[9]-=-.� �� � � �� � � � � � 14 CLARK BARWICK Scholium 2.3 (Dwyer–Kan). — Suppose Q : M �Mc a cofibrant replacement functor, R : M �Mf a fibrant replacement functor, Γ• : M � (cM)c a cosimplicial resolutio... |

17 | Homotopy theory of model categories. Unpublished manuscript, available electronically from http://www-math.mit.edu/~psh/#Reedy - Reedy |

5 |
localizations of categories
- Simplicial
- 1980
(Show Context)
Citation Context ...bjects are exactly those of M, with Mor L H M(X, Y ) = colimn ν•(w Mor n M(X, Y )) for any objects X and Y . The standard references on the hammock localization are the triple of papers [6], [7], and =-=[8]-=- of W. G. Dwyer and D. Kan. A more modern treatment can be found in [9].� �� � � �� � � � � � 14 CLARK BARWICK Scholium 2.3 (Dwyer–Kan). — Suppose Q : M �Mc a cofibrant replacement functor, R : M �Mf... |

2 | Higher topos theory. Unpublished manuscript, available on the arXiv as arXiv:math/0608040 - Lurie - 2007 |

1 |
Weak M-categories I
- Barwick
- 2007
(Show Context)
Citation Context ...me, but it may be the case that there are one or two results that have not become part of the conventional wisdom. This very brief note was culled — with only mild changes — from my forthcoming books =-=[1]-=- and [2] on higher categories and weak enrichments. I have decided to make some results available separately, in deference those who apparently wish to use the some of the techniques before the long p... |

1 | Borceux – Handbook of categorical algebra. 2, Encyclopedia of Mathematics and its - unknown authors - 1994 |

1 |
Combinatorial model categories”, To exist. 12 August 2007
- Smith
(Show Context)
Citation Context ...ause the morphism R MorM(colim B, Z) �� R MorM(colim A, Z) is a homotopy limit of weak equivalences in sSetX, hence a weak equivalence. � �� �� �� � � �� �� � � 16 CLARK BARWICK Theorem 2.11 (Smith, =-=[16]-=-). — If M is X-combinatorial, and H is an X-small set of homotopy classes of morphisms of M, the left Bousfield localization LHM of M along any set representing H exists and satisfies the following co... |