Grothendieck quasitoposes
| Autor: | Richard Garner, Stephen Lack |
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| Rok vydání: | 2011 |
| Předmět: |
Separated object
Pure mathematics Algebra and Number Theory Concrete sheaf Presheaf Mathematics - Category Theory Network topology Quasitopos Topos theory Set (abstract data type) Topos Reflection (mathematics) Mathematics::Algebraic Geometry If and only if Localization Mathematics::Category Theory FOS: Mathematics Semi-left-exact reflection Category Theory (math.CT) Reflective subcategory Topology (chemistry) Mathematics |
| DOI: | 10.48550/arxiv.1106.5331 |
| Popis: | A full reflective subcategory E of a presheaf category [C*,Set] is the category of sheaves for a topology j on C if and only if the reflection preserves finite limits. Such an E is called a Grothendieck topos. More generally, one can consider two topologies, j contained in k, and the category of sheaves for j which are separated for k. The categories E of this form, for some C, j, and k, are the Grothendieck quasitoposes of the title, previously studied by Borceux and Pedicchio, and include many examples of categories of spaces. They also include the category of concrete sheaves for a concrete site. We show that a full reflective subcategory E of [C*,Set] arises in this way for some j and k if and only if the reflection preserves monomorphisms as well as pullbacks over elements of E. Comment: v2: 24 pages, several revisions based on suggestions of referee, especially the new theorem 5.2; to appear in the Journal of Algebra |
| Databáze: | OpenAIRE |
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