Semisimplicity manifesting as categorical smallness
Why this work is in the frame
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Bibliographic record
Abstract
For a compact group G, the functor from unital Banach algebras with contractive morphisms to metric spaces with 1-Lipschitz maps sending a Banach algebra A to the space of G-representations in A preserves filtered colimits.Along with this, we prove a number of analogues: one can substitute unitary representations in C algebras, as well as semisimple finite-dimensional Banach algebras (or finite-dimensional C -algebras) for G.These all mimic results on the metric-enriched finite generation/presentability of finitedimensional Banach spaces due to Admek and Rosick.We also give an alternative proof of that finite presentability result, along with parallel results on functors represented by compact metric, metric convex, or metric absolutely convex spaces. Frequently (e.g.[1, I, p.84], [58, Paragraph following Theorem 12.2.2],[2, Definition 5.9]) to Cpc, q preserving certain transfinite chains of morphisms in a given class (one often also speaks of compact objects in that context). In additive categories the term sometimes [48, 3.5, Proposition 5.1 and sentence following it] means that Cpc, q preserves arbitrary coproducts (so filtered colimits of split embeddings).Thanks are due to M. Brannan for numerous enlightening exchanges and M. Reyes for invaluable help in gaining access to some of the cited literature.
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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 | 0.001 |
| 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 | 0.000 |
| 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