Morphisms of 2-groupoids and low-dimensional cohomology of crossed modules
Bibliographic record
Abstract
Given a morphism P : G → H of 2-groupoids, we construct a 6-term 2-exact sequence of cat-groups and pointed groupoids. We use this sequence to obtain an analogue for cat-groups (and, in particular, for crossed modules) of the fundamental exact sequence of non-abelian group cohomology. The link with simplicial topology is also explained. Introduction The aim of this paper is to obtain a basic result in low-dimensional cohomology of crossed modules. Homology and cohomology of crossed modules have been studied extensively, and a satisfactory theory has been developed (see [7] and the references therein, [14, 19, 20, 26]). The existing literature on this subject considers crossed modules and their morphisms as a category. Our point of view is that crossed modules are in a natural way the objects of a 2-category, and therefore they should be studied in a 2-dimensional context. This different point of view leads to 1991 Mathematics Subject Classification. Primary 18G50; Secondary 18B40, 18D05, 18D35, 20L05. Third author supported by FNRS grant 1.5.116.01. c ©0000 American Mathematical Society
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.000 | 0.003 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 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".