Bibliographic record
Abstract
Sheaves are objects of a local nature: a global section is determined by how it looks locally.Hence, a sheaf cannot describe mathematical structures which contain global or nonlocal geometric information.To fill this gap, we introduce the theory of "gleaves", which are presheaves equipped with an additional "gluing operation" of compatible pairs of local sections.This generalizes the conditional product structures of Dawid and Studený, which correspond to gleaves on distributive lattices.Our examples include the gleaf of metric spaces and the gleaf of joint probability distributions.A result of Johnstone shows that a category of gleaves can have a subobject classifier despite not being cartesian closed.Gleaves over the simplex category ∆, which we call compositories, can be interpreted as a new kind of higher category in which the composition of an m-morphism and an n-morphism along a common k-morphism face results in an (m + n -k)-morphism.The distinctive feature of this composition operation is that the original morphisms can be recovered from the composite morphism as initial and final faces.Examples of compositories include nerves of categories and compositories of higher spans.
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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 | 0.002 |
| 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 | 0.007 |
| Scholarly communication | 0.003 | 0.009 |
| Open science | 0.000 | 0.005 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 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".