Bibliographic record
Abstract
We show that factorization systems, both strict and orthogonal, can be equivalently described as double categories satisfying certain properties.This provides conceptual reasons for why the category of sets and partial maps or the category of small categories and cofunctors admit orthogonal factorization systems.The theory also gives an explicit description of various lax morphism classifiers and explains why they admit strict factorization systems.In a general double category you cannot compose vertical morphisms with horizontal ones, but if you could, you might interpret the above square α as telling us that the morphism v g (horizontal followed by vertical) can be factored as h u (vertical followed by horizontal) -this is reminiscent of ordinary factorization systems on a category.Taking this philosophy to heart, we assign to a double category X a certain category of corners CnrpXq (a concept introduced by Mark Weber in [Weber15]), in which composition of vertical and horizontal morphisms is possible, and for which squares in X turn into commutative squares in CnrpXq.Regarding the double category as a diagram X : ∆ op Ñ Cat, producing CnrpXq amounts to taking the codescent object of X, a 2-categorical colimit that is an analogue of ordinary coequalizers.
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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 | 0.002 |
| 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 | 0.003 | 0.005 |
| Open science | 0.000 | 0.004 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.009 | 0.001 |
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".