Bibliographic record
Abstract
For a category C, a small category I, and a pre-cover relation ⊏ on C we prove, under certain completeness assumptions on C, that a morphism g : B → C in the functor category C I has an ⊏ I -image, where ⊏ I is the pre-cover relation on C I induced by ⊏, as soon as each component of g has an ⊏-image.We then apply this to show that if a pointed category C is: (i) algebraically cartesian closed; (ii) exact protomodular and action accessible; or (iii) admits normalizers, then the same is true of each functor category C I with I finite.In addition, our results give explicit constructions of ⊏ I -images in functor categories using limits and ⊏-images in the underlying category.In particular, they can be used to give explicit constructions of both centralizers and normalizers in functor categories using limits and centralizers or normalizers (respectively) in the underlying category.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.003 | 0.009 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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".