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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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>𝒞</mml:mi> </mml:math> , corresponding to the category of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>𝒞</mml:mi> </mml:math> -diagrams on the cylinder. We also give an alternative characterization in terms of adjoining dot generators to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>𝒞</mml:mi> </mml:math> . 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>𝒞</mml:mi> </mml:math> 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 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)0.001
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow)
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 score0.141
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.001
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.001
Research integrity0.0010.002
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 head0.022
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 teacher head, not a consensus.

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

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