Bibliographic record
Abstract
We present two generalizations of the Span construction.The first generalization gives Span of a category with all pullbacks as a (weak) double category.This double category Span A can be viewed as the free double category on the vertical category A where every vertical arrow has both a companion and a conjoint (and these companions and conjoints are adjoint to each other).Thus defined, Span : Cat Doub becomes a 2-functor, which is a partial left bi-adjoint to the forgetful functor Vrt : Doub Cat, which sends a double category to its category of vertical arrows.The second generalization gives Span of an arbitrary category as an oplax normal double category.The universal property can again be given in terms of companions and conjoints and the presence of their composites.Moreover, Span A is universal with this property in the sense that Span : Cat OplaxNDoub is left bi-adjoint to the forgetful functor which sends an oplax double category to its vertical arrow category.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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".