A projective model structure on pro-simplicial sheaves, and the relative étale homotopy type

Fibrations and Homotopy Colimits of Simplicial Sheaves

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 no...

A Model Structure on the Category of Pro-simplicial Sets

We study the category pro-SS of pro-simplicial sets, which arises in étale homotopy theory, shape theory, and pro-finite completion. We establish a model structure on pro-SS so that it is possible to do homotopy theory in this category. This model structure is closely related to the strict structure of Edwards and Hastings. In order to understand the notion of homotopy groups for pro-spaces we ...

Homotopy theory of simplicial sheaves in completely decomposable topologies

On the structure of A-Homotopy sheaves I

A Unramified sheaves of groups over finite fields 74 0 Introduction This paper is the first part of a series of two papers, with sequel [27]. The problem addressed in these two works is to understand the analogue in the context of the A 1-homotopy theory of smooth schemes over a field k constructed in [41, 30] of the following classical facts from algebraic topology:

the investigation of the relationship between type a and type b personalities and quality of translation

چکیده ندارد.