Bibliographic record
Abstract
We present a doctrinal approach to category theory, obtained by abstracting from the indexed inclusion (via discrete fibrations and opfibrations) of left and of right actions of X ∈ Cat in categories over X. Namely, a "weak temporal doctrine" consists essentially of two indexed functors with the same codomain such that the induced functors have both left and right adjoints satisfying some exactness conditions, in the spirit of categorical logic.The derived logical rules include some adjunction-like laws involving the truth-valuesenriched hom and tensor functors, which condense several basic categorical properties and display a nice symmetry.The symmetry becomes more apparent in the slightly stronger context of "temporal doctrines", which we initially treat and which include as an instance the inclusion of lower and upper sets in the parts of a poset, as well as the inclusion of left and right actions of a graph in the graphs over it.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.003 | 0.008 |
| Scholarly communication | 0.006 | 0.010 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.009 | 0.002 |
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".