### Abstract

Closed model categories for presheaves of simplicial groupoids and presheaves of 2-groupoids by Zhi-ming Luo

### Citations

343 |
Homotopical algebra
- Quillen
- 1967
(Show Context)
Citation Context ...on A Quillen closed model category D is a category which is equipped with three classes of morphisms, called cofibrations, fibrations and weak equivalences which together satisfy the following axioms =-=[9]-=-, [10], [3]: CM1: The category D is closed under all finite limits and colimits. CM2: Suppose that the following diagram commutes in D: X ⏐ ⏐ ↓h Z g −→ ր f Y If any two of f, g and h are weak equivale... |

228 |
Rational homotopy theory
- Quillen
- 1969
(Show Context)
Citation Context ...Quillen closed model category D is a category which is equipped with three classes of morphisms, called cofibrations, fibrations and weak equivalences which together satisfy the following axioms [9], =-=[10]-=-, [3]: CM1: The category D is closed under all finite limits and colimits. CM2: Suppose that the following diagram commutes in D: X ⏐ ⏐ ↓h Z g −→ ր f Y If any two of f, g and h are weak equivalences, ... |

117 |
Simplicial presheaves
- Jardine
- 1987
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Citation Context ...osed model structures. For example, the category of simplicial groupoids by Dwyer-Kan [2], [3] , the category of 2-groupoids by Moerdijk-Svensson [8], the category of simplicial presheaves by Jardine =-=[5]-=-, the category of simplicial sheaves by Joyal [7] and so on. Crans [1] uses adjoint functors to prove that a kind of sheaves have closed model structures according to a well-known closed model categor... |

23 |
Algebraic classification of equivariant homotopy 2-types
- Moerdijk, Svensson
- 1993
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Citation Context ...e found a large quantity of categories enjoying the closed model structures. For example, the category of simplicial groupoids by Dwyer-Kan [2], [3] , the category of 2-groupoids by Moerdijk-Svensson =-=[8]-=-, the category of simplicial presheaves by Jardine [5], the category of simplicial sheaves by Joyal [7] and so on. Crans [1] uses adjoint functors to prove that a kind of sheaves have closed model str... |

20 |
Homotopy Theory of Simplicial Groupoids
- Dwyer, Kan
- 1984
(Show Context)
Citation Context ...al sets has a closed model structure [9]. Mathematicians have found a large quantity of categories enjoying the closed model structures. For example, the category of simplicial groupoids by Dwyer-Kan =-=[2]-=-, [3] , the category of 2-groupoids by Moerdijk-Svensson [8], the category of simplicial presheaves by Jardine [5], the category of simplicial sheaves by Joyal [7] and so on. Crans [1] uses adjoint fu... |

15 | Quillen closed model structures for sheaves
- Crans
- 1995
(Show Context)
Citation Context ...ds by Dwyer-Kan [2], [3] , the category of 2-groupoids by Moerdijk-Svensson [8], the category of simplicial presheaves by Jardine [5], the category of simplicial sheaves by Joyal [7] and so on. Crans =-=[1]-=- uses adjoint functors to prove that a kind of sheaves have closed model structures according to a well-known closed model category. We use similar technique, basing on Jardine’s paper [5], to prove t... |

2 |
Boolean Localization
- Jardine
- 1996
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Citation Context ...ious. ✷ There exists a Kan Ex ∞ functor from SPre(C) to SPre(C), such that Ex ∞ X is locally fibrant for any simplicial presheaf X and the canonical map ν : X → Ex ∞ X is a pointwise weak equivalence =-=[6]-=-. Fix a Boolean localization ℘ : Shv(B) → E, and consider the functors SPre(C) L2 −→ SE ℘∗ −→ SShv(B) relating the categories of simplicial presheaves on C and the categories of simplicial sheaves and... |

2 |
letter to A.Grothendieck
- Joyal
- 1984
(Show Context)
Citation Context ...of simplicial groupoids by Dwyer-Kan [2], [3] , the category of 2-groupoids by Moerdijk-Svensson [8], the category of simplicial presheaves by Jardine [5], the category of simplicial sheaves by Joyal =-=[7]-=- and so on. Crans [1] uses adjoint functors to prove that a kind of sheaves have closed model structures according to a well-known closed model category. We use similar technique, basing on Jardine’s ... |