Bibliographic record
Abstract
We consider pre-exponentiable objects of a pre-cartesian double category D, i.e., objects Y such that the lax functor - Y : D G G D has a right adjoint in the 2-category LxDbl of double categories and lax functors.When D has 2-glueing (in the sense of [N12a]), we show that Y is pre-exponentiable in D if and only if Y is exponentiable in D 0 and - Y is an oplax functor.Thus, such a D is pre-cartesian closed as a double category if and only if D 0 is a cartesian closed category.Applications include the double categories Cat, Pos, Top, Loc, and Topos, whose objects are small categories, posets, topological space, locales, and toposes, respectively.D, i.e., Y such that the lax functor - Y : D G G D has a right adjoint in the 2-category LxDbl.We restrict to right adjoints in LxDbl rather than PsDbl because, in some of our examples (e.g., Cat and Pos), the right adjoints that exist are not pseudo even though D is cartesian, i.e., - Y is pseudo.The five examples of interest here are double categories D with 2-glueing, in the sense of [N12a, N12b], which is a common generalization of Artin-Wraith glueing for toposes [J77] and a special case of Bnabou's equivalence Lax N (B, Prof ) Cat/B used by Street
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| 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".