Fibrations and Homotopy Colimits of Simplicial Sheaves
نویسنده
چکیده
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 notion of a quasi-fibration of spaces, and seems to be of independent interest.
منابع مشابه
A-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...
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