MétaCan
Menu
Back to cohort
Record W3093747925 · doi:10.5802/jep.158

Affinization of monoidal categories

2021· preprint· en· W3093747925 on OpenAlexfundno aff
Youssef Mousaaid, Alistair Savage

Bibliographic record

VenueJournal de l’École polytechnique — Mathématiques · 2021
Typepreprint
Languageen
FieldMathematics
TopicAlgebraic structures and combinatorial models
Canadian institutionsnot available
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsBraidTRACE (psycholinguistics)MathematicsKnot (papermaking)Pure mathematicsSymmetric monoidal categoryCharacterization (materials science)Enriched categoryAlgebra over a fieldCombinatoricsFunctorPhysicsLinguistics

Abstract

fetched live from OpenAlex

We define the affinization of an arbitrary monoidal category 𝒞 , corresponding to the category of 𝒞 -diagrams on the cylinder. We also give an alternative characterization in terms of adjoining dot generators to 𝒞 . The affinization formalizes and unifies many constructions appearing in the literature. In particular, we describe a large number of examples coming from Hecke-type algebras, braids, tangles, and knot invariants. When 𝒞 is rigid, its affinization is isomorphic to its horizontal trace, although the two definitions look quite different. In general, the affinization and the horizontal trace are not isomorphic.

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)0.002
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 score0.008
Threshold uncertainty score0.026

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.002
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0040.002
Science and technology studies0.0040.004
Scholarly communication0.0030.006
Open science0.0010.004
Research integrity0.0010.002
Insufficient payload (model declined to judge)0.0080.002

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 head0.022
GPT teacher head0.300
Teacher spread0.278 · 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

Citations0
Published2021
Admission routes1
Has abstractyes

Explore more

Same venueJournal de l’École polytechnique — MathématiquesSame topicAlgebraic structures and combinatorial modelsFrench-language works237,207