Triple

T13660579
Position Surface form Disambiguated ID Type / Status
Subject Picard–Vessiot theory E326982 entity
Predicate isRelatedTo P37 FINISHED
Object Tannakian categories
Tannakian categories are rigid, abelian, tensor categories that generalize the representation theory of affine group schemes and provide a categorical framework for Galois-type dualities.
E1053929 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: Tannakian categories | Statement: [Picard–Vessiot theory, isRelatedTo, Tannakian categories]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Tannakian categories
Context triple: [Picard–Vessiot theory, isRelatedTo, Tannakian categories]
  • A. Grothendieck duality
    Grothendieck duality is a foundational theory in algebraic geometry that generalizes classical Serre duality to a broad categorical and sheaf-theoretic framework for studying duality on schemes and morphisms.
  • 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. Deligne–Lusztig theory
    Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
  • D. Adeles and Algebraic Groups
    "Adeles and Algebraic Groups" is a foundational mathematical work by André Weil that develops the theory of adeles and its deep connections with algebraic groups and number theory.
  • E. Deligne cohomology
    Deligne cohomology is a refined cohomology theory in algebraic geometry that combines singular cohomology and differential forms to capture both topological and arithmetic information about complex algebraic varieties.
  • 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: Tannakian categories
Triple: [Picard–Vessiot theory, isRelatedTo, Tannakian categories]
Generated description
Tannakian categories are rigid, abelian, tensor categories that generalize the representation theory of affine group schemes and provide a categorical framework for Galois-type dualities.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Tannakian categories
Target entity description: Tannakian categories are rigid, abelian, tensor categories that generalize the representation theory of affine group schemes and provide a categorical framework for Galois-type dualities.
  • A. Grothendieck duality
    Grothendieck duality is a foundational theory in algebraic geometry that generalizes classical Serre duality to a broad categorical and sheaf-theoretic framework for studying duality on schemes and morphisms.
  • 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. Deligne–Lusztig theory
    Deligne–Lusztig theory is a framework in algebraic geometry and representation theory that constructs and studies representations of finite groups of Lie type using varieties defined over finite fields.
  • D. Adeles and Algebraic Groups
    "Adeles and Algebraic Groups" is a foundational mathematical work by André Weil that develops the theory of adeles and its deep connections with algebraic groups and number theory.
  • E. Deligne cohomology
    Deligne cohomology is a refined cohomology theory in algebraic geometry that combines singular cohomology and differential forms to capture both topological and arithmetic information about complex algebraic varieties.
  • 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_69d8076d8270819092afc2f0e9c359a8 completed April 9, 2026, 8:09 p.m.
NER Named-entity recognition batch_69dbc620df208190afaccf3ddd10aa60 completed April 12, 2026, 4:19 p.m.
NED1 Entity disambiguation (via context triple) batch_69f78b08d27c8190badc612c26423c0e completed May 3, 2026, 5:51 p.m.
NEDg Description generation batch_69f78fd0d29481908bd44bda28e3b2c1 completed May 3, 2026, 6:11 p.m.
NED2 Entity disambiguation (via description) batch_69f7908d92e08190918525c59cb37b55 completed May 3, 2026, 6:14 p.m.
Created at: April 9, 2026, 9:52 p.m.