Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Projective Model Structure on Pro Simplicial Sheaves, and the Relative
  \'Etale Homotopy Type   In this work we shall introduce a new model structure on the category of
pro-simplicial sheaves, which is very convenient for the study of \'etale
homotopy. Using this model structure we define a pro-space associated to a
topos, as a result of applying a derived functor. We show that our construction
lifts Artin and Mazur's \'etale homotopy type [AM] in the relevant special
case. Our definition extends naturally to a relative notion, namely, a
pro-object associated to a map of topoi. This relative notion lifts the
relative \'etale homotopy type that was used in [HaSc] for the study of
obstructions to the existence of rational points. This relative notion enables
to generalize these homotopical obstructions from fields to general base
schemas and general maps of topoi.
  Our model structure is constructed using a general theorem that we prove.
Namely, we introduce a much weaker structure than a model category, which we
call a "weak fibration category". Our theorem says that a weak fibration
category can be "completed" into a full model category structure on its
pro-category, provided it satisfies some additional technical requirements. Our
model structure is obtained by applying this result to the weak fibration
category of simplicial sheaves over a Grothendieck site, where the weak
equivalences and the fibrations are local in the sense of Jardine [Jar].

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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga