A construction of certain weak colimits and an exactness property of the 2-category of categories
Bibliographic record
Abstract
Given a 2-category A, a 2-functor A F -→ Cat and a distinguished 1-subcategory Σ ⊂ A containing all the objects, a σ-cone for F (with respect to Σ) is a lax cone such that the structural 2-cells corresponding to the arrows of Σ are invertible.The conical σ-limit is the universal (up to isomorphism) σ-cone.The notion of σ-limit generalizes the well known notions of pseudo and lax limit.We consider the fundamental notion of σ-filtered pair (A, Σ) which generalizes the notion of 2-filtered 2-category.We give an explicit construction of σ-filtered σ-colimits of categories, a construction which allows computations with these colimits.We then state and prove a basic exactness property of the 2-category of categories, namely, that σ-filtered σ-colimits commute with finite weighted pseudo (or bi) limits.An important corollary of this result is that a σ-filtered σ-colimit of exact category valued 2-functors is exact.This corollary is essential in the 2-dimensional theory of flat and pro-representable 2-functors, that we develop elsewhere.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.001 | 0.003 |
| 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".