Pivotality, twisted centres, and the anti-double of a Hopf monad
Bibliographic record
Abstract
Finite-dimensional Hopf algebras admit a correspondence between socalled pairs in involution, one-dimensional anti-Yetter-Drinfeld modules and algebra isomorphisms between the Drinfeld and anti-Drinfeld double.We extend it to general rigid monoidal categories and provide a monadic interpretation under the assumption that certain coends exist.Hereto we construct and study the anti-Drinfeld double of a Hopf monad.As an application the connection with the pivotality of Drinfeld centres and their underlying categories is discussed.We would like to thank Ilya Shaprio for many fruitful discussions in the early stages of this project and Kenichi Shimizu for helpful remarks concerning symmetric centres and connections to topological quantum field theories.We further thank the anonymous referee for many useful remarks, suggestions, and improvements.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
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".