Triple

T10773152
Position Surface form Disambiguated ID Type / Status
Subject Grothendieck topology E254130 entity
Predicate hasAlternativeFormulation P3660 FINISHED
Object Grothendieck pretopology
A Grothendieck pretopology is a way of specifying covering families on a category that generates a Grothendieck topology and is often more convenient to work with in practice.
E254130 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Grothendieck pretopology | Statement: [Grothendieck topology, hasAlternativeFormulation, Grothendieck pretopology]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Grothendieck pretopology
Context triple: [Grothendieck topology, hasAlternativeFormulation, Grothendieck pretopology]
  • A. Grothendieck topology
    A Grothendieck topology is an abstract framework in category theory that generalizes the notion of open covers in topology to define sheaves on arbitrary categories.
  • B. Grothendieck toposes
    Grothendieck toposes are highly structured categories that generalize topological spaces and serve as a unifying framework for geometry, logic, and cohomology in modern mathematics.
  • C. Grothendieck category
    A Grothendieck category is an abelian category with exact filtered colimits and a generator, providing a highly general framework that extends the properties of module and sheaf categories in homological algebra.
  • D. Grothendieck universe
    A Grothendieck universe is a set-theoretic construct large enough to contain all the usual objects and operations of mathematics, used to rigorously handle "large" categories while avoiding paradoxes.
  • E. Sheaves in Geometry and Logic
    Sheaves in Geometry and Logic is a foundational monograph that develops the theory of sheaves and topos theory and explores their deep connections to geometry, logic, and the foundations of mathematics.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Grothendieck pretopology
Triple: [Grothendieck topology, hasAlternativeFormulation, Grothendieck pretopology]
Generated description
A Grothendieck pretopology is a way of specifying covering families on a category that generates a Grothendieck topology and is often more convenient to work with in practice.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Grothendieck pretopology
Target entity description: A Grothendieck pretopology is a way of specifying covering families on a category that generates a Grothendieck topology and is often more convenient to work with in practice.
  • A. Grothendieck topology chosen
    A Grothendieck topology is an abstract framework in category theory that generalizes the notion of open covers in topology to define sheaves on arbitrary categories.
  • B. Grothendieck toposes
    Grothendieck toposes are highly structured categories that generalize topological spaces and serve as a unifying framework for geometry, logic, and cohomology in modern mathematics.
  • C. Grothendieck category
    A Grothendieck category is an abelian category with exact filtered colimits and a generator, providing a highly general framework that extends the properties of module and sheaf categories in homological algebra.
  • D. Grothendieck universe
    A Grothendieck universe is a set-theoretic construct large enough to contain all the usual objects and operations of mathematics, used to rigorously handle "large" categories while avoiding paradoxes.
  • E. Sheaves in Geometry and Logic
    Sheaves in Geometry and Logic is a foundational monograph that develops the theory of sheaves and topos theory and explores their deep connections to geometry, logic, and the foundations of mathematics.
  • F. None of above.

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69d6aa5f54f4819082d0bbcb6f8797e6 completed April 8, 2026, 7:19 p.m.
NER Named-entity recognition batch_69d7329b27748190bd0e2569c7972fd1 completed April 9, 2026, 5:01 a.m.
NED1 Entity disambiguation (via context triple) batch_69de238559b48190abc759e744ab0f8e completed April 14, 2026, 11:22 a.m.
NEDg Description generation batch_69de271fb08c8190a44c547083226fd8 completed April 14, 2026, 11:38 a.m.
NED2 Entity disambiguation (via description) batch_69de2cecc24c8190a240366e0600426a completed April 14, 2026, 12:02 p.m.
Created at: April 8, 2026, 9:16 p.m.