Bibliographic record
Abstract
A generating family in a category C is a collection of objects {A i |i ∈ I} such that if for any subobject Y / / m / / X, every A i f / / X factors through m, then m is an isomorphism -i.e. the functors C(A i , ) are collectively conservative.In this paper, we examine some circumstances under which subobjects of 1 form a generating family.Objects for which subobjects of 1 do form a generating family are called partially well-pointed.For a Grothendieck topos, it is well known that subobjects of 1 form a generating family if and only if the topos is localic.For the elementary case, little more is known.The problem is studied in [1], where it is shown that the result is internally true, an equivalent condition is found in the boolean case, and certain preservation properties are shown.We look at two different approaches to the problem, one based on a generalization of projectivity, and the other based on looking at the most extreme sorts of counterexamples.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".