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.