Fibrations and homotopy colimits of simplicial sheaves

Abstract

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.

Cited by in corpus (13)

• Simplicial structures on model categories and functors
• Homotopy theory for algebras over polynomial monads
• On the Q construction for exact quasicategories
• All $(\infty ,1)$-toposes have strict univalent universes
• Fibre sequences and localization of simplicial sheaves
• A Quillen Theorem B for strict $\infty$-categories
• Classifying spaces and fibrations of simplicial sheaves
• The Local Joyal Model Structure
• Nonabelian mixed Hodge structures
• Categorifying measure theory: a roadmap
• Motivic Cell Structures for Spherical Varieties
• An extension of Quillen's Theorem B
• On the Evrard fibrant replacement of a functor