Bibliographic record
Abstract
Precategories generalize both the notions of strict n-category and sesquicategory: their definition is essentially the same as the one of strict n-categories, excepting that the various interchange laws are not required to hold.Those have been proposed as a framework in which one can express semi-strict definitions of weak higher categories.In particular, in dimension 3, Gray categories are particular 3-precategories which have been shown to be equivalent to tricategories.In this article, we are mostly interested in free precategories.Those can be presented by generators and relations, using an appropriate variation on the notion of polygraph (aka computad), and earlier works have shown that the theory of rewriting can be generalized to this setting, enjoying most of the fundamental constructions and properties which can be found in the traditional theory: with respect to this, polygraphs for precategories are much better behaved than their counterpart for strict categories.We further study here why this is the case, by providing several results which show that precategories and their associated polygraphs bear properties which ensure that we have a good syntax for those.In particular, we show that the category of polygraphs for precategories form a presheaf category.Contents 1 Precategories and their polygraphs 788 2 Free functors are Conduch 793 3 Makkai's criterion for presheaf categories 800 4 The support function 802 5 Polyplexes 804 6 Polygraphs as a presheaf category 811 7 Parametric adjunction and generic factorization 813 8 Toward homotopical properties of precategories 815
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 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".