  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.
