Bibliographic record
Abstract
A pair of objects (P, Q) in a monoidal category C, is called a pivotal pair if there exist a family of duality morphisms, making Q both a left dual and a right dual of P .We introduce the correct notion of morphisms between such pairs, and thereby define the pivotal cover of a monoidal category.Given such a pair (P, Q), we construct the category C(P, Q), of objects which intertwine with P and Q in a compatible manner and show that C(P, Q) lifts the monoidal structure of C as well as the closed structure of C, when C is closed.If C has suitable colimits, we construct a family of Hopf monads which correspond to such pairs in C and present the resulting families of braided Hopf algebras and Hopf algebroids, when C is a braided category or the category of bimodules over a base algebra, respectively.
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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 | 0.000 |
| 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".