Triple

T17386421
Position Surface form Disambiguated ID Type / Status
Subject Jacob Lurie E422697 entity
Predicate notableWork P4 FINISHED
Object Higher Topos Theory
Higher Topos Theory is a foundational monograph in modern algebraic topology and higher category theory that develops the theory of ∞-topoi and their applications to homotopy theory and algebraic geometry.
 E1266017 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: Higher Topos Theory | Statement: [Jacob Lurie, notableWork, Higher Topos Theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Higher Topos Theory
Context triple: [Jacob Lurie, notableWork, Higher Topos Theory]
  • A. 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.
  • B. Sketches of an Elephant: A Topos Theory Compendium
    Sketches of an Elephant: A Topos Theory Compendium is a comprehensive, multi-volume reference work on topos theory that systematically develops and surveys the subject at an advanced research level.
  • C. 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.
  • D. 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.
  • E. Théorie des topos et cohomologie étale des schémas
    Théorie des topos et cohomologie étale des schémas is a foundational multi-volume work in algebraic geometry, originating from Grothendieck’s Séminaire de Géométrie Algébrique, that develops topos theory and étale cohomology of schemes.
  • 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: Higher Topos Theory
Triple: [Jacob Lurie, notableWork, Higher Topos Theory]
Generated description
Higher Topos Theory is a foundational monograph in modern algebraic topology and higher category theory that develops the theory of ∞-topoi and their applications to homotopy theory and algebraic geometry.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Higher Topos Theory
Target entity description: Higher Topos Theory is a foundational monograph in modern algebraic topology and higher category theory that develops the theory of ∞-topoi and their applications to homotopy theory and algebraic geometry.
  • A. 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.
  • B. Sketches of an Elephant: A Topos Theory Compendium
    Sketches of an Elephant: A Topos Theory Compendium is a comprehensive, multi-volume reference work on topos theory that systematically develops and surveys the subject at an advanced research level.
  • C. 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.
  • D. 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.
  • E. Théorie des topos et cohomologie étale des schémas
    Théorie des topos et cohomologie étale des schémas is a foundational multi-volume work in algebraic geometry, originating from Grothendieck’s Séminaire de Géométrie Algébrique, that develops topos theory and étale cohomology of schemes.
  • 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_69d889d710288190bf0f4762801fefae completed April 10, 2026, 5:25 a.m.
NER Named-entity recognition batch_69e43a8a93f48190a31f5cc58d950758 completed April 19, 2026, 2:14 a.m.
NED1 Entity disambiguation (via context triple) batch_6a019ff95e7c81909564abc3fe319611 completed May 11, 2026, 9:23 a.m.
NEDg Description generation batch_6a01a0c2f1108190b3cdabdcd3da7253 completed May 11, 2026, 9:26 a.m.
NED2 Entity disambiguation (via description) batch_6a01a14aeab881908abf4ec28164ba84 completed May 11, 2026, 9:28 a.m.
Created at: April 10, 2026, 5:45 a.m.