### Citations

297 |
Complexe cotangent et deformations. I,
- Illusie
- 1971
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Citation Context ...f the cotangent complex Lf associated to any morphism f : A→ B of commutative rings was worked on by several people, including André [1], Quillen [23], Lichtenbaum and Schlessinger [18], and Illusie =-=[13]-=-. Later, Schwede introduced cotangent complexes in more generality [25], by introducing spectra in DERIVED SMOOTH MANIFOLDS 33 model categories and showing that Lf emerges in a canonical way when one ... |

215 |
Iterated path integrals,
- Chen
- 1977
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Citation Context ...stacks on derived manifolds, but we have not worked out this idea. 10.3. Chen spaces, diffeological spaces. Another common generalization of the category of manifolds was invented by Kuo Tsai Chen in =-=[8]-=-. Let Conv denote the category whose objects are convex subsets of R∞, and whose morphisms are smooth maps. With the Grothendieck topology in which coverings are given by open covers in the usual sens... |

161 | Model categories and their localizations, volume 99 of Mathematical Surveys and Monographs. - Hirschhorn - 2003 |

148 |
Model categories, volume 63 of Mathematical Surveys and Monographs.
- Hovey
- 1999
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Citation Context ...d for doing intersection theory on manifolds, in the sense of Definition 2.1. Convention 4.1. In this paper we will rely heavily on the theory of model categories and their localizations. See [11] or =-=[12]-=- for a good introduction to this subject. If X is a category, there are two common model structures on the simplicial presheaf category sSetsX , called the injective and the projective model structure... |

62 | Hypercovers and simplicial presheaves.
- Dugger, Isaksen
- 2004
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Citation Context ...ven sections. Jardine showed in [14] that there is a model category structure on sSetsOp(X) op in which the fibrant objects are homotopy sheaves on X ; we denote this model category Shv(X, sSets). In =-=[10]-=-, the authors show that Shv(X, sSets) is a localization of the injective model structure on sSetsOp(X) op at a certain set of morphisms (called the hypercovers) to obtain Shv(X, sSets). From this, one... |

61 | Handbook of categorical algebra. 2, volume 51 of Encyclopedia of Mathematics and its Applications - Borceux - 1994 |

45 | Topology and geometry, volume 139 of Graduate Texts in Mathematics - Bredon - 1993 |

36 | Methode simpliciale en algebre homologique et algebre commutative, - Andre - 1967 |

17 | On (enriched) left Bousfield localizations of model categories. Preprint arxiv: 0708.2067
- Barwick
- 2007
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Citation Context ... proper, combinatorial, simplicial model category. As stated above, weak equivalences and cofibrations are determined object-wise; in particular every object in sSetsX is cofibrant. See, for example, =-=[4]-=- or [20] for further details. 5. C∞-rings Let E denote the full subcategory of Man spanned by the Euclidean spaces Ri, for i ∈ N; we refer to E as the Euclidean category. Lawvere, Dubuc, Moerdijk and ... |

17 |
Hirschhorn,Model categories and their localizations
- S
- 2003
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Citation Context ...er that the object in the upper left corner is a pullback in the usual sense. Two objects are equivalent if and only if they are isomorphic. Remark 1.2. If C is a simplicial model category (see, e.g. =-=[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. Moreover, we can replace any diagram wit... |

5 | C ∞ -schemes - Dubuc - 1981 |

4 | Archimedian local C ∞ -rings and models of synthetic differential geometry. Cahiers Topologie Géom - Bunge, Dubuc - 1986 |

2 |
Sminaire de Gomtrie Algbrique du Bois Marie - Thorie des topos et cohomologie tale des schmas - (SGA 4), volume 269
- Artin, Grothendieck, et al.
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Citation Context ...” on ringed spaces. Considering sections of the structure sheaf as functions to affine space, a ringed space is local if these functions pull covers back to covers. This point of view can be found in =-=[2]-=- and [7], for example. Recall the notation |F | = F (R) for a C∞-ring F ; see Notation 6.12. Recall also that C∞(R) denotes the free (discrete) C∞-ring on one generator. Definition 8.7. Let X be a top... |

2 |
Convenient categories of smooth spaces. ePrint available: http://front.math.ucdavis.edu/0807.1704
- Baez, Hoffnung
- 2008
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Citation Context ... topos Shv(Conv). The category of Chen spaces is roughly this topos, the difference being that points are given more importance in Chen spaces than in Shv(Conv), in a sense known as concreteness (see =-=[3]-=- for a precise account). Diffeological spaces are similar – they are defined roughly as sheaves on the category of open subsets of Euclidean spaces. The difference between these approaches and our own... |

2 |
André,Méthode simpliciale en algèbre homologique et algèbre commutative
- unknown authors
- 1967
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Citation Context ...ients derived cobordisms similarly. All results which we prove in the unoriented case also work in the oriented case. Remark 3.9. One can show that if U is an open neighborhood of the closed interval =-=[0, 1]-=- ⊂ R then any proper map f : X → U can be extended to a proper map g : X → R with an isomorphism f−1([0, 1]) ∼= g−1([0, 1]) over [0, 1]. So, one can consider such an f to be a derived cobordism betwee... |

2 |
Archimedian local C∞-rings and models of synthetic differential geometry. Cahiers Topologie Géom
- Bunge, Dubuc
- 1986
(Show Context)
Citation Context ...ged spaces. Considering sections of the structure sheaf as functions to affine space, a ringed space is local if these functions pull covers back to covers. This point of view can be found in [2] and =-=[7]-=-, for example. Recall the notation |F | = F (R) for a C∞-ring F ; see Notation 6.12. Recall also that C∞(R) denotes the free (discrete) C∞-ring on one generator. Definition 8.7. Let X be a topological... |