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Record W4405527322 · doi:10.1016/j.jpaa.2024.107859

An inductive model structure for strict ∞-categories

2024· article· en· W4405527322 on OpenAlexaff
Simon Henry, Félix Loubaton

Bibliographic record

VenueJournal of Pure and Applied Algebra · 2024
Typearticle
Languageen
FieldMathematics
TopicHomotopy and Cohomology in Algebraic Topology
Canadian institutionsUniversity of Ottawa
FundersAgence Nationale de la Recherche
KeywordsMathematicsAlgebra over a fieldCalculus (dental)Pure mathematics

Abstract

fetched live from OpenAlex

We construct a left semi-model category of “marked strict ∞-categories” for which the fibrant objects are those whose marked arrows satisfy natural closure properties and are invertible up to higher marked arrows. The canonical model structure on strict ∞-categories can be recovered as a left Bousfield localization of this model structure. We show that an appropriate extension of the Street nerve to the marked setting produces a Quillen adjunction between our model category and the Verity model structure for complicial sets, generalizing previous results by the second named author. Finally, we use this model structure to study, in the setting of strict ∞-categories, the idea that, because they are two different “truncation functors” taking an ( ∞ , n ) to an ( ∞ , n − 1 ) -category, there are two non-equivalent definitions for the ( ∞ , 1 ) -category of ( ∞ , ∞ ) -categories as a limit of the ( ∞ , 1 ) -categories of ( ∞ , n ) -categories. We show that in fact there seem to be at least three non-equivalent ways of constructing an ( ∞ , 1 ) -category of ( ∞ , ∞ ) -categories.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.001
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.004
Threshold uncertainty score0.013

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.001
Bibliometrics0.0010.001
Science and technology studies0.0010.004
Scholarly communication0.0020.006
Open science0.0010.004
Research integrity0.0010.002
Insufficient payload (model declined to judge)0.0040.001

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.025
GPT teacher head0.305
Teacher spread0.280 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

Quick stats

Citations2
Published2024
Admission routes1
Has abstractyes

Explore more

Same venueJournal of Pure and Applied AlgebraSame topicHomotopy and Cohomology in Algebraic TopologyFrench-language works237,207