Bibliographic record
Abstract
To 2-categorify the theory of group representations, we introduce the notions of the 3-representation of a group in a strict 3-category and the strict 2-categorical action of a group on a strict 2-category.We also 2-categorify the concept of the trace by introducing the 2-categorical trace of a 1-endomorphism in a strict 3-category.For a 3-representation ρ of a group G and an element f of G, the 2-categorical trace Tr 2 ρ f is a category.Moreover, the centralizer of f in G acts categorically on this 2-categorical trace.We construct the induced strict 2-categorical action of a finite group, and show that the 2-categorical trace Tr 2 takes an induced strict 2-categorical action into an induced categorical action of the initia groupoid.As a corollary, we get the 3-character formula of the induced strict 2-categorical action.Contents 1 Introduction 1999 2 The 3-representations of groups 2002 3 The 2-categorical traces of 3-representations 2016 4 The induced strict 2-categorical action on the induced 2-category 2026 5 The 3-character of the induced strict 2-categorical action 2029 6 The categorical action of the centralizer of f on Tr 2 ρ f 2034
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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 | 0.001 | 0.007 |
| Scholarly communication | 0.002 | 0.007 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| 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".