Triple

T2290649
Position Surface form Disambiguated ID Type / Status
Subject Alexander Grothendieck E51493 entity
Predicate notableConcept P201 FINISHED
Object 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.
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 topology | Statement: [Alexander Grothendieck, notableConcept, Grothendieck topology]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Grothendieck topology
Context triple: [Alexander Grothendieck, notableConcept, Grothendieck topology]
  • A. 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.
  • B. 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.
  • C. Categories for the Working Mathematician
    Categories for the Working Mathematician is a foundational textbook in category theory that systematically develops the subject and its applications for professional mathematicians.
  • D. Zariski topology
    The Zariski topology is a fundamental topology in algebraic geometry, defined on the spectrum of a ring or an algebraic variety, whose closed sets correspond to solution sets of polynomial equations.
  • E. Alexandrov–Čech cohomology
    Alexandrov–Čech cohomology is a topological cohomology theory that computes invariants of spaces using inverse limits over open covers, closely related to and often coinciding with sheaf cohomology.
  • 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 topology
Triple: [Alexander Grothendieck, notableConcept, Grothendieck topology]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Grothendieck topology
Target entity description: 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.
  • A. 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.
  • B. 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.
  • C. Categories for the Working Mathematician
    Categories for the Working Mathematician is a foundational textbook in category theory that systematically develops the subject and its applications for professional mathematicians.
  • D. Zariski topology
    The Zariski topology is a fundamental topology in algebraic geometry, defined on the spectrum of a ring or an algebraic variety, whose closed sets correspond to solution sets of polynomial equations.
  • E. Alexandrov–Čech cohomology
    Alexandrov–Čech cohomology is a topological cohomology theory that computes invariants of spaces using inverse limits over open covers, closely related to and often coinciding with sheaf cohomology.
  • F. None of above. chosen

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_69a88b09c644819090b503456d96bf70 completed March 4, 2026, 7:42 p.m.
NER Named-entity recognition batch_69abc27536588190a74731b5537c90ee completed March 7, 2026, 6:15 a.m.
NED1 Entity disambiguation (via context triple) batch_69ae7f210bb881909086b86b2c3017a7 completed March 9, 2026, 8:04 a.m.
NEDg Description generation batch_69ae8018c2e88190aaacaad9adc442cf completed March 9, 2026, 8:08 a.m.
NED2 Entity disambiguation (via description) batch_69ae806fd8008190bfd6c6bcd1d0ddbd completed March 9, 2026, 8:10 a.m.
Created at: March 4, 2026, 7:48 p.m.