An étalé space construction for stacks
| Autor: | David Carchedi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Pure mathematics
étale stack topoi Topological space Topos theory étalé space Mathematics::Algebraic Geometry 58H05 Stack (abstract data type) topos Mathematics::Category Theory Equivalence (formal languages) topological stack 22A22 Mathematics Fixed base Zariski topology action groupoid 14A20 groupoid 18B25 18F20 53C08 Sheaf Geometry and Topology differentiable stack |
| Zdroj: | Algebr. Geom. Topol. 13, no. 2 (2013), 831-903 |
| Popis: | We generalize the notion of a sheaf of sets over a space to define the notion of a small stack of groupoids over an étale stack. We then provide a construction analogous to the étalé space construction in this context, establishing an equivalence of [math] –categories between small stacks over an étale stack and local homeomorphisms over it. These results hold for a wide variety of types of spaces, for example, topological spaces, locales, various types of manifolds, and schemes over a fixed base (where stacks are taken with respect to the Zariski topology). Along the way, we also prove that the [math] –category of topoi is fully reflective in the [math] –category of localic stacks. |
| Databáze: | OpenAIRE |
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