Bibliographic record
Abstract
A PROP is a way of encoding structure borne by an object of a symmetric monoidal category.We describe a notion of distributive law for PROPs, based on Beck's distributive laws for monads.A distributive law between PROPs allows them to be composed, and an algebra for the composite PROP consists of a single object with an algebra structure for each of the original PROPs, subject to compatibility conditions encoded by the distributive law.An example is the PROP for bialgebras, which is a composite of the PROP for coalgebras and that for algebras.The original version of this paper contained the false identification of PROPs with morphisms P → T of PROs.Thanks are due to Fabio Zanasi [14], who noticed this error.The current version has been corrected in paragraphs 2.4, 4.3, and 4.4.
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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 | 0.004 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.004 | 0.012 |
| Open science | 0.001 | 0.009 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.013 | 0.004 |
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".