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In algebraic geometry, a prestack F over a category C equipped with some Grothendieck topology is a category together with a functor p: F → C satisfying a certain lifting condition and such that (when the fibers are groupoids) locally isomorphic objects are isomorphic. A stack is a prestack with effective descents, meaning local objects may be patched together to become a global object.

Attributes	Values
rdf:type	Thing
rdfs:label	Prestack (en)
rdfs:comment	In algebraic geometry, a prestack F over a category C equipped with some Grothendieck topology is a category together with a functor p: F → C satisfying a certain lifting condition and such that (when the fibers are groupoids) locally isomorphic objects are isomorphic. A stack is a prestack with effective descents, meaning local objects may be patched together to become a global object. (en)
rdfs:seeAlso	Morphism of algebraic stacks
dcterms:subject	Algebraic geometry
Wikipage page ID	39547490 (xsd:integer)
Wikipage revision ID	1065648632 (xsd:integer)
Link from a Wikipage to another Wikipage	Morphism of schemes Algebraic group Algebraic space Presheaf (category theory) Natural transformation Quotient stack Quotient by an equivalence relation Deligne–Mumford stack Functor category Stack (mathematics) Algebraic geometry Equivalence relation Torsor (algebraic geometry) Algebraic geometry Coequalizer Grothendieck topology Groupoid Groupoid scheme Injective function Étale topology Fibered category Classifying stack Slice category Yoneda's lemma Projectivized vector bundle Smooth topology (algebraic geometry) Stack associated to a scheme Sheaf of sets Sheafification dbr:2-Yoneda_lemma dbr:2-quotient
Link from a Wikipage to an external page	http://www.math.unizh.ch/index.php%3Fpr_vo_det&key1=1287&key2=580&no_cache=1%7Cfirst1=Kai%7Clast1=Behrend%7Cfirst2=Brian%7Clast2=Conrad%7Cfirst3=Dan%7Clast3=Edidin%7Cfirst4=William%7Clast4=Fulton%7Cfirst5=Barbara%7Clast5=Fantechi%7Cfirst6=Lothar%7Clast6=G%C3%B6ttsche%7Cfirst7=Andrew%7Clast7=Kresch%7Cyear=2006%7Ctitle=Algebraic https://mathoverflow.net/q/3119 https://web.archive.org/web/20080505043444/http:/www.math.unizh.ch/index.php%3Fpr_vo_det&key1=1287&key2=580&no_cache=1%23%7Carchive-date=2008-05-05%7Curl-status=dead
sameAs	Prestack Prestack
dbp:wikiPageUsesTemplate	dbt:' dbt:Citation dbt:Cite_web dbt:Ordered_list dbt:Reflist dbt:See_also dbt:Short_description
has abstract	In algebraic geometry, a prestack F over a category C equipped with some Grothendieck topology is a category together with a functor p: F → C satisfying a certain lifting condition and such that (when the fibers are groupoids) locally isomorphic objects are isomorphic. A stack is a prestack with effective descents, meaning local objects may be patched together to become a global object. Prestacks that appear in nature are typically stacks but some naively constructed prestacks (e.g., groupoid scheme or the prestack of projectivized vector bundles) may not be stacks. Prestacks may be studied on their own or . Since a stack is a prestack, all the results on prestacks are valid for stacks as well. Throughout the article, we work with a fixed base category C; for example, C can be the category of all schemes over some fixed scheme equipped with some Grothendieck topology. (en)
prov:wasDerivedFrom	wikipedia-en:Prestack?oldid=1065648632&ns=0
page length (characters) of wiki page	21873 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Prestack
is Link from a Wikipage to another Wikipage of	Canonical map Morphism of algebraic stacks Pseudo-functor Glossary of category theory Stack (mathematics) Differentiable stack Torsor (algebraic geometry) Coherency (homotopy theory) Groupoid object Stackification Pre-stack
is Wikipage redirect of	Stackification Pre-stack
is foaf:primaryTopic of	wikipedia-en:Prestack

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