Bibliographic record
Abstract
Certain aspects of Street's formal theory of monads in 2-categories are extended to multimonoidal monads in symmetric strict monoidal 2-categories.Namely, any symmetric strict monoidal 2-category M admits a symmetric strict monoidal 2category of pseudomonoids, monoidal 1-cells and monoidal 2-cells in M. Dually, there is a symmetric strict monoidal 2-category of pseudomonoids, opmonoidal 1-cells and opmonoidal 2-cells in M. Extending a construction due to Aguiar and Mahajan for M Cat, we may apply the first construction p-times and the second one q-times (in any order).It yields a 2-category M pq .A 0-cell therein is an object A of M together with p q compatible pseudomonoid structures; it is termed a pp qq-oidal object in M. A monad in M pq is called a pp, qq-oidal monad in M; it is a monad t on A in M together with p monoidal, and q opmonoidal structures in a compatible way.If M has monoidal Eilenberg-Moore construction, and certain (Linton type) stable coequalizers exist, then a pp qq-oidal structure on the Eilenberg-Moore object A t of a pp, qq-oidal monad pA, tq is shown to arise via a symmetric strict monoidal double functor to Ehresmann's double category SqrpMq of squares in M, from the double category of monads in SqrpMq in the sense of Fiore, Gambino and Kock.While q ones of the pseudomonoid structures of A t are lifted along the 'forgetful' 1-cell A t Ñ A, the other p ones are lifted along its left adjoint.In the particular example when M is an appropriate 2-subcategory of Cat, this yields a conceptually different proof of some recent results due to Aguiar, Haim and López Franco.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot 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.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".