Fibre Sequences and Localization of Simplicial Sheaves
نویسنده
چکیده
In this paper, we provide criteria for fibre sequences of simplicial sheaves to be preserved by nullifications. This generalizes a result of Berrick and Dror Farjoun and allows a better understanding of unstable A-homotopy theory.
منابع مشابه
Classifying Spaces and Fibrations of Simplicial Sheaves
In this paper, we discuss the construction of classifying spaces of fibre sequences in model categories of simplicial sheaves. One construction proceeds via Brown representability and provides a classification in the pointed model category. The second construction is given by the classifying space of the monoid of homotopy self-equivalences of a simplicial sheaf and provides the unpointed class...
متن کاملA-homotopy theory of schemes
2 Homotopy category of a site with interval 2 2.1 Homotopy theory of simplicial sheaves . . . . . . . . . . . . . . 4 2.1.1 Simplicial sheaves . . . . . . . . . . . . . . . . . . . . . 4 2.1.2 The simplicial model category structure . . . . . . . . 5 2.1.3 Local fibrations and resolution lemmas . . . . . . . . . 8 2.1.4 Homotopy limits and colimits. . . . . . . . . . . . . . . 12 2.1.5 Eilenber...
متن کاملConstructible Sheaves on Simplicial Complexes and Koszul Duality
We obtain a linear algebra data presentation of the category Sh c (X,δ) of constructible with respect to perverse triangulation sheaves on a finite simplicial complex X. We also establish Koszul duality between Sh c (X, δ) and the category Mc(X, δ) of perverse sheaves constructible with respect to the triangulation
متن کاملFibrations and Homotopy Colimits of Simplicial Sheaves
We show that homotopy pullbacks of sheaves of simplicial sets over a Grothendieck topology distribute over homotopy colimits; this generalizes a result of Puppe about topological spaces. In addition, we show that inverse image functors between categories of simplicial sheaves preserve homotopy pullback squares. The method we use introduces the notion of a sharp map, which is analogous to the no...
متن کاملA Model Category for Local Po-spaces
Locally partial-ordered spaces (local po-spaces) have been used to model concurrent systems. We provide equivalences for these spaces by constructing a model category containing the category of local po-spaces. We show the category of simplicial presheaves on local po-spaces can be given Jardine’s model structure, in which we identify the weak equivalences between local po-spaces. In the proces...
متن کامل