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Record W4413972877 · doi:10.70930/tac/ow4l40au

Notes on Bimonads and Hopf Monads

2012· article· en· W4413972877 on OpenAlexvenueno aff
Bachuki Mesablishvili, Robert Wisbauer

Bibliographic record

VenueTheory and applications of categories · 2012
Typearticle
Languageen
FieldMathematics
TopicAdvanced Topics in Algebra
Canadian institutionsnot available
FundersDeutsche Forschungsgemeinschaft
KeywordsMathematicsComputer science

Abstract

fetched live from OpenAlex

For a generalisation of the classical theory of Hopf algebra over fields, A. Bruguires and A. Virelizier study opmonoidal monads on monoidal categories (which they called bimonads).In a recent joint paper with S. Lack the same authors define the notion of a pre-Hopf monad by requiring only a special form of the fusion operator to be invertible.In previous papers it was observed by the present authors that bimonads yield a special case of an entwining of a pair of functors (on arbitrary categories).The purpose of this note is to show that in this setting the pre-Hopf monads are a special case of Galois entwinings.As a byproduct some new properties are detected which make a (general) bimonad on a Cauchy complete category to a Hopf monad.In the final section applications to cartesian monoidal categories are considered.

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 score0.182
Threshold uncertainty score0.292

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 head0.313
Teacher spread0.287 · 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

Citations1
Published2012
Admission routes1
Has abstractyes

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