"Fibrations and homotopy colimits of simplicial sheaves"
Charles Rezk
(Primary 18G30; Secondary 18B25, 55R99)
Department of Mathematics
Northwestern University
Evanston, IL 60208
rezk@math.nwu.edu
November 3, 1998
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.