Bibliographic record
Abstract
‘Sets for Mathematics’, by F.W. Lawvere and R. Rosebrugh, [5] is a ground-breaking, undergraduate, set theory textbook. Categories provide the metalanguage and, for a substantial part of the book, axioms are gradually imposed on a category S until its objects and arrows capture the key features of sets and functions that are used in mathematical practice. To those who would say that sets and functions are themselves lurking in the definition of category , the rejoinder should surely be that sets and functions are present to the same extent in the metalanguage of traditional set theory texts. By the time a student starts to think critically about sets and functions in an undergraduate mathematics program, he or she has already implicitly studied several categories—continuous, differentiable, linear, order-preserving, and so on. It is to these categories, and other categories of mathematical structures, that a student turns repeatedly in the course of studying Mathematics. To see these categories as categories of sets with structure, it seems to this writer most appropriate to put the formal study of sets themselves on the same footing. Lawvere and Rosebrugh accomplish in [5] much more than is possible in a traditional set theory book because they isolate those categorical axioms for sets and functions that allow sets to admit both variation and the intuitionistically valid constructs and theorems of the subject. A category satisfying the axioms in question is called a(n elementary ) topos .
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 | 0.001 | 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 | 0.005 |
| Scholarly communication | 0.005 | 0.007 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.014 | 0.003 |
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".