Familial 2-functors and parametric right adjoints
Why this work is in the frame
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Bibliographic record
Abstract
We define and study familial 2-functors primarily with a view to the development of the 2-categorical approach to operads of [Weber, 2005].Also included in this paper is a result in which the well-known characterisation of a category as a simplicial set via the Segal condition, is generalised to a result about nice monads on cocomplete categories.Instances of this general result can be found in [Leinster, 2004], [Berger, 2002] and [Moerdijk-Weiss, 2007b].Aspects of this general theory are then used to show that the composite 2-monads of [Weber, 2005] that describe symmetric and braided analogues of the -operads of [Batanin, 1998], are cartesian 2-monads and their underlying endo-2-functor is familial.Intricately linked to the notion of familial 2-functor is the theory of fibrations in a finitely complete 2-category [Street, 1974] [Street, 1980a], and those aspects of that theory that we require, that weren't discussed in [Weber, 2007], are reviewed here.
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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 | 0.001 | 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