The purpose of this paper is to develop a theory of \((\infty , 1)\)-stacks, in the sense of Hirschowitz–Simpson’s ‘Descent Pour Les n–Champs’, using the language of quasi-category theory and the author’s local Joyal model structure. The main result is a characterization of \((\infty , 1)\)-stacks in terms of mapping space presheaves. An important special case of this theorem gives a sufficient condition for the presheaf of quasi-categories associated to a presheaf of model categories to be a higher stack. In the final section, we apply this result to construct the higher stack of unbounded complexes associated to a ringed site.

本文的目的是使用准类别理论的语言和Hirschowitz-Simpson的“ Descent Pour Les n-Champs”，发展一个\（（\ infty，1）\）-堆栈的理论。作者的本地Joyal模型结构。主要结果是对\（（\ infty，1）\）- stacks的映射空间映射。该定理的一个重要特例为与模型类别的预捆相关的准类别的预捆成为更高的堆栈提供了充分的条件。在最后一节中，我们将这个结果应用于构建与环状位点关联的无边界复合物的更高堆栈。