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A presheaf on a site satisfying the local identity and unique gluing condition for every cover.
This node means a sheaf of sets on a site. Sheaves valued in groups, rings, modules, or other categories are modeled by the corresponding algebraic-object nodes.
wp-sheaf-ringsnlab-sheafstacks-sheafEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Require matching local sections to glue uniquely over every cover.
Feed several structures into a construction junction and impose compatibility between them.
stacks-sheafwp-sheafnlab-sheafstacks-schemes-textEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Specialize to an fppf sheaf on , require a representable diagonal, and require that some scheme admit a surjective étale morphism .
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
stacks-algebraic-spaceThis is an authored directed relation from the source endpoint to the target endpoint.
Equip every section set with compatible group structure.
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
stacks-abelian-sheafwp-sheaf-groupsstacks-schemes-textThis is an authored directed relation from the source endpoint to the target endpoint.
Equip every section set with compatible ring structure.
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
stacks-sheaf-algebraicwp-sheaf-ringsstacks-schemes-textThis is an authored directed relation from the source endpoint to the target endpoint.
The stalk is the filtered colimit over neighborhoods of the point.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
stacks-schemes-text