### Abstract

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

### Citations

324 |
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: g X �� � Y ��� � h �� �� f ������ Z If any two of f,g and h are ... |

114 |
Simplicial presheaves
- Jardine
- 1987
(Show Context)
Citation Context ...losed model structures. For example, the category of simplicial groupoids by Dwyer-Kan [2], [3] , the category of 2-groupoids by MoerdijkSvensson [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... |

22 |
Algebraic classification of equivariant homotopy 2-types. 1
- Moerdijk, Svensson
- 1993
(Show Context)
Citation Context ...ve 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 MoerdijkSvensson =-=[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 and simplicial groupoids, Nederl
- 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 MoerdijkSvensson [8], the category of simplicial presheaves by Jardine [5], the category of simplicial sheaves by Joyal [7] and so on. Crans [1] uses adjoint fun... |

14 | Quillen closed model structures for sheaves
- Crans
- 1995
(Show Context)
Citation Context ...ids by Dwyer-Kan [2], [3] , the category of 2-groupoids by MoerdijkSvensson [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... |

4 |
Rational homotopy theory, Ann. of Math. 90
- 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: g X �� � Y ��� � h �� �� f ������ Z If any two of f,g and h are weak e... |

2 |
Boolean Localization
- Jardine
- 1996
(Show Context)
Citation Context ...bvious. 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 MoerdijkSvensson [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 ... |