Bibliographic record
Abstract
If C and D are varieties of algebras in the sense of general algebra, then by a representable functor C → D we understand a functor which, when composed with the forgetful functor D → Set, gives a representable functor in the classical sense; Freyd showed that these functors are determined by D-coalgebra objects of C. Let Rep(C, D) denote the category of all such functors, a full subcategory of Cat(C, D), opposite to the category of D-coalgebras in C.It is proved that Rep(C, D) has small colimits, and in certain situations, explicit constructions for the representing coalgebras are obtained.In particular, Rep(C, D) always has an initial object.This is shown to be "trivial" unless C and D either both have no zeroary operations, or both have more than one derived zeroary operation.In those two cases, the functors in question may have surprisingly opulent structures.It is also shown that every set-valued representable functor on C admits a universal morphism to a D-valued representable functor.Several examples are worked out in detail, and areas for further investigation are noted.In § §1-7 below we develop our general results, and in § §9-14, some examples.(One example is also worked in §5, to motivate the ideas of §6.)R. Paré has pointed out to me that my main result, Theorem 4.6, can be deduced from [19, Theorem 6.1.4,p.143, and following remark, and ibid.Corollary 6.2.5, p.149].However, as he observes, it is useful to have a direct proof.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.005 | 0.001 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.001 | 0.006 |
| Research integrity | 0.001 | 0.002 |
| 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".