Fibrations and homotopy colimits of simplicial sheaves

Details Fibrations and homotopy colimits of simplicial sheaves Fibrations and homotopy colimits of simplicial sheaves

1998-11-06

arxiv.org/abs/math/9811038v2

Mathematics

Algebraic Topology

Scientific paper

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.

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