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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 distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation 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: Empirical
Teacher disagreement score0.031
Threshold uncertainty score0.483

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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 teacher head, 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