Bibliographic record
Abstract
Following the many splendid mathematical discoveries of the nineteenth century, mathematicians like Felix Hausdorff and Emmy Noether formalized the key-notions and thereby the categories which enable us to pursue modern structural mathematics. Bourbaki's monumental work gives the most comprehensive testimony of this rapid development during the first half of the twentieth century. Despite the laudable trend toward emphasizing applications, for the past few decades there has been little change in the overall perception of which general notions are to be considered important, and they continue to dominate the standard courses on topology and algebra. Soon after Samuel Eilenberg and Saunders Mac Lane coined the notions of category, functor and natural transformation in the 1940s, a very different way of doing structural mathematics emerged which was promoted especially in homo-logical algebra. Rather than building objects made up from sets with a structure, like topological spaces and modules over a ring, one imposes additional conditions on a category which make its objects behave like the structured sets one has in mind. Hence, rather than relying on a set-theoretic foundation on which to build the structures at issue, one moves into a “fully equipped building” in which to explore the objects of interest. Indeed, the category theory of the 1950s, especially Alexander Grothendieck's work, showed that a great deal of module theory can be performed in any abelian category and which abelian categories are actually-equivalent to module categories.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.290 | 0.152 |
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".