What is the universal property of the 2-category of monads?
Bibliographic record
Abstract
For a 2-category K, we consider Street's 2-category Mnd(K) of monads in K, along with Lack and Street's 2-category EM(K) and the identity-on-objects-and-1cells 2-functor Mnd(K) → EM(K) between them.We show that this 2-functor can be obtained as a "free completion" of the 2-functor 1 : K → K.We do this by regarding 2-functors which act as the identity on both objects and 1-cells as categories enriched a cartesian closed category BO whose objects are identity-on-objects functors.We also develop some of the theory of BO-enriched categories.The first-named author acknowledges with gratitude the support of an Australian Research Council Discovery Project DP190102432, and the second-named author an MQRES PhD Scholarship, 20192497.We are happy to acknowledge useful conversations with John Power on the topic of the paper; AM is also grateful to Charles Walker for discussions around the connection with double categories.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.003 | 0.012 |
| Scholarly communication | 0.004 | 0.016 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 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".