1998/11/06 by Charles Rezk, Rezk, Charles · 1 citation
Computer Science · Mathematics · #18B25 #18G30 (Primary) #55R99 (Secondary) #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #math.CT #msc:18B25 #msc:18G30 #msc:55R99
paper · pdf · doi:10.48550/arxiv.math/9811038
openalex publication_date 1998/11/06 · arxiv created 1998/11/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.