Bibliographic record
Abstract
. In analogy with the varietal case, we give an abstract characterization of those categories occurring as regular epireflective subcategories of presheaf categories such that the inclusion functor preserves small sums. The aim of this short note is to add one step to the nice parallelism between presheaf categories and algebraic categories. Presheaf categories can be abstractly characterized as exact and extensive categories with a small set of indecomposable, regular projective regular generators (Bunge [1]) (here extensive means with disjoint and universal small sums, and indecomposable means that each morphism from a generator to a small sum of generators factors through one of the canonical injections). Bearing in mind this characterization, Giraud's axioms for Grothendieck toposes become transparent: drop the assumptions which are not stable under localization (observe that the extensivity assumption, which is a little bit redundant in Bunge's theorem, is essential in Giraud'...
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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 | 0.000 |
| 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".