Lax comma 2-categories and admissible 2-functors
Bibliographic record
Abstract
This paper is a contribution towards a two dimensional extension of the basic ideas and results of Janelidze's Galois theory.In the present paper, we give a suitable counterpart notion to that of absolute admissible Galois structure for the lax idempotent context, compatible with the context of lax orthogonal factorization systems.As part of this work, we study lax comma 2-categories, giving analogue results to the basic properties of the usual comma categories.We show that each morphism of a 2-category induces a 2-adjunction between lax comma 2-categories and comma 2-categories, playing the role of the usual change-of-base functors.With these induced 2-adjunctions, we are able to show that each 2-adjunction induces 2-adjunctions between lax comma 2-categories and comma 2-categories, which are our analogues of the usual lifting to the comma categories used in Janelidze's Galois theory.We give sufficient conditions under which these liftings are 2-premonadic and induce a lax idempotent 2monad, which corresponds to our notion of 2-admissible 2-functor.In order to carry out this work, we analyse when a composition of 2-adjunctions is a lax idempotent 2-monad, and when it is 2-premonadic.We give then examples of our 2-admissible 2-functors (and, in particular, simple 2-functors), especially using a result that says that all admissible (2-)functors in the classical sense are also 2-admissible (and hence simple as well).
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 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 | 0.001 | 0.004 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".