Triple

T15918654
Position Surface form Disambiguated ID Type / Status
Subject George Bergman E386035 entity
Predicate notableWork P4 FINISHED
Object Invitation to General Algebra and Universal Constructions
"Invitation to General Algebra and Universal Constructions" is a graduate-level mathematics textbook by George Bergman that introduces general algebraic structures and category-theoretic methods, emphasizing universal properties and constructions.
E1182415 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: Invitation to General Algebra and Universal Constructions | Statement: [George Bergman, notableWork, Invitation to General Algebra and Universal Constructions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Invitation to General Algebra and Universal Constructions
Context triple: [George Bergman, notableWork, Invitation to General Algebra and Universal Constructions]
  • A. 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.
  • B. “Abelian Categories: An Introduction to the Theory of Functors”
    “Abelian Categories: An Introduction to the Theory of Functors” is a foundational monograph in category theory that systematically develops the theory of abelian categories and functors, significantly shaping modern homological algebra.
  • C. Moderne Algebra
    Moderne Algebra is a foundational 20th-century textbook that systematically developed abstract algebra and helped shape the modern axiomatic approach to the subject.
  • D. A Survey of Modern Algebra
    A Survey of Modern Algebra is a classic and influential textbook that systematically introduces the fundamental concepts and structures of modern abstract algebra.
  • 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: Invitation to General Algebra and Universal Constructions
Triple: [George Bergman, notableWork, Invitation to General Algebra and Universal Constructions]
Generated description
"Invitation to General Algebra and Universal Constructions" is a graduate-level mathematics textbook by George Bergman that introduces general algebraic structures and category-theoretic methods, emphasizing universal properties and constructions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Invitation to General Algebra and Universal Constructions
Target entity description: "Invitation to General Algebra and Universal Constructions" is a graduate-level mathematics textbook by George Bergman that introduces general algebraic structures and category-theoretic methods, emphasizing universal properties and constructions.
  • A. 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.
  • B. “Abelian Categories: An Introduction to the Theory of Functors”
    “Abelian Categories: An Introduction to the Theory of Functors” is a foundational monograph in category theory that systematically develops the theory of abelian categories and functors, significantly shaping modern homological algebra.
  • C. Moderne Algebra
    Moderne Algebra is a foundational 20th-century textbook that systematically developed abstract algebra and helped shape the modern axiomatic approach to the subject.
  • D. A Survey of Modern Algebra
    A Survey of Modern Algebra is a classic and influential textbook that systematically introduces the fundamental concepts and structures of modern abstract algebra.
  • 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

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_69d86da686e4819097cbf3b1fc2d881d completed April 10, 2026, 3:25 a.m.
NER Named-entity recognition batch_69e1567ff9e48190b73cb101fc3f7b2b completed April 16, 2026, 9:37 p.m.
NED1 Entity disambiguation (via context triple) batch_69ffb05d1fb481909b42bea774a15c70 completed May 9, 2026, 10:08 p.m.
NEDg Description generation batch_69ffb0cfac808190b32bb25659603fb4 completed May 9, 2026, 10:10 p.m.
NED2 Entity disambiguation (via description) batch_69ffb15b987c8190ae9c96f15fc55b27 completed May 9, 2026, 10:12 p.m.
Created at: April 10, 2026, 4:52 a.m.