Bibliographic record
Abstract
It is known that a topological correspondence (X, ) from a locally compact groupoid with a Haar system (G, ) to another one, (H, ), produces a C * -correspondence H(X, ) from C * (G, ) to C * (H, ).We described the composition of two topological correspondences in one of our earlier articles.In the present article, we prove that second countable locally compact Hausdorff groupoids with Haar systems form a bicategory T when equipped with topological correspondences as 1-arrows and isomorphisms of topological correspondences as 2-arrows.On the other hand, it well-known that C * -algebras form a bicategory C with C *correspondences as 1-arrows, and the unitary isomorphisms of Hilbert C * -modules that intertwine the representations serve as the 2-arrows.In this article, we show that a topological correspondence going to a C * -one is a bifunctor T / / C. Finally, we show that in the sub-bicategory of T consisting of the Macho-Stadler-O'uchi correspondences, invertible 1-arrows are exactly the groupoid equivalences.
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How this classification was reachedexpand
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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".