Notes on enriched categories with colimits of some class
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Bibliographic record
Abstract
The paper is in essence a survey of categories having -weighted colimits for all the weights in some class .We introduce the class + of -flat weights which are those for which -colimits commute in the base V with limits having weights in ; and the class -of -atomic weights, which are those for which -limits commute in the base V with colimits having weights in .We show that both these classes are saturated (that is, what was called closed in the terminology of [AK88]).We prove that for the class P of all weights, the classes P + and P -both coincide with the class Q of absolute weights.For any class and any category A, we have the free -cocompletion (A) of A; and we recognize Q(A) as the Cauchy-completion of A. We study the equivalence between (Q(A op ))op and Q(A), which we exhibit as the restriction of the Isbell adjunction between [A, V]op and [A op , V] when A is small; and we give a new Morita theorem for any class containing Q.We end with the study of -continuous weights and their relation to the -flat weights.
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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 it