Bibliographic record
Abstract
This paper concerns the relationships between notions of weak n-category defined as algebras for n-globular operads, as well as their coherence properties.We focus primarily on the definitions due to Batanin and Leinster.A correspondence between the contractions and systems of compositions used in Batanin's definition, and the unbiased contractions used in Leinster's definition, has long been suspected, and we prove a conjecture of Leinster that shows that the two notions are in some sense equivalent.We then prove several coherence theorems which apply to algebras for any operad with a contraction and system of compositions or with an unbiased contraction; these coherence theorems thus apply to weak n-categories in the senses of Batanin, Leinster, Penon and Trimble.We then take some steps towards a comparison between Batanin weak n-categories and Leinster weak n-categories.We describe a canonical adjunction between the categories of these, giving a construction of the left adjoint, which is applicable in more generality to a class of functors induced by monad morphisms.We conclude with some preliminary statements about a possible weak equivalence of some sort between these 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 | 0.004 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.001 | 0.005 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".